<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-02-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000726854</issuerCik>
        <issuerName>CITY HOLDING CO</issuerName>
        <issuerTradingSymbol>CHCO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001296026</rptOwnerCik>
            <rptOwnerName>DERITO JOHN A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>25 GATEWATER ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CROSS LANES</rptOwnerCity>
            <rptOwnerState>WV</rptOwnerState>
            <rptOwnerZipCode>25313</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, Commercial Banking</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20972</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-02-27</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>645</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>645.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>645</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>657.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>657</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>37.74</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2018-02-27</value>
            </exerciseDate>
            <expirationDate>
                <value>2023-02-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>38.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>38</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>44.43</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2018-03-26</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-03-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>807.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>807</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
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            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2019-03-26</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-03-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>807.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1614</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>46.61</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2018-02-26</value>
            </exerciseDate>
            <expirationDate>
                <value>2025-02-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>600.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>600</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>46.61</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2019-02-26</value>
            </exerciseDate>
            <expirationDate>
                <value>2025-02-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>600.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1200</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>46.61</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2020-02-26</value>
            </exerciseDate>
            <expirationDate>
                <value>2025-02-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>600.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1800</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>43.73</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2019-02-24</value>
            </exerciseDate>
            <expirationDate>
                <value>2026-02-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>977.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>977</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>43.73</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2020-02-24</value>
            </exerciseDate>
            <expirationDate>
                <value>2026-02-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>977.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1954</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>43.73</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2021-02-24</value>
            </exerciseDate>
            <expirationDate>
                <value>2026-02-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>977.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2933</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>66.32</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2020-02-22</value>
            </exerciseDate>
            <expirationDate>
                <value>2027-02-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1033.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1033</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>66.32</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2021-02-22</value>
            </exerciseDate>
            <expirationDate>
                <value>2027-02-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1033.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2066</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>66.32</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2022-02-22</value>
            </exerciseDate>
            <expirationDate>
                <value>2027-02-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1034.0</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3100</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each restricted stock unit represents the right to receive, at settlement, one share of common stock.</footnote>
        <footnote id="F2">One-third of these restricted stock units are scheduled to vest on each of February 27, 2020; February 27, 2021; and February 27, 2022.</footnote>
        <footnote id="F3">One-third of these restricted stock units are scheduled to vest on each of February 28, 2019; February 28, 2020; and February 28, 2021.</footnote>
        <footnote id="F4">Options shares granted from City Holding Company's 2013 Incentive Plan are subject to both time-based and performance-based vesting.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Victoria A. Faw, attorney-in-fact</signatureName>
        <signatureDate>2019-02-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2019-02-27
0
0000726854
CITY HOLDING CO
CHCO
0001296026
DERITO JOHN A
25 GATEWATER ROAD
CROSS LANES
WV
25313
0
1
0
0
EVP, Commercial Banking
Common Stock
20972
D
Common Stock
0.0
2019-02-27
4
A
0
645
0
A
Common Stock
645.0
645
D
Restricted Stock Unit
0.0
Common Stock
657.0
657
D
Stock Option to Buy
37.74
2018-02-27
2023-02-26
Common Stock
38.0
38
D
Stock Option to Buy
44.43
2018-03-26
2024-03-25
Common Stock
807.0
807
D
Stock Option to Buy
44.43
2019-03-26
2024-03-25
Common Stock
807.0
1614
D
Stock Option to Buy
46.61
2018-02-26
2025-02-25
Common Stock
600.0
600
D
Stock Option to Buy
46.61
2019-02-26
2025-02-25
Common Stock
600.0
1200
D
Stock Option to Buy
46.61
2020-02-26
2025-02-25
Common Stock
600.0
1800
D
Stock Option to Buy
43.73
2019-02-24
2026-02-23
Common Stock
977.0
977
D
Stock Option to Buy
43.73
2020-02-24
2026-02-23
Common Stock
977.0
1954
D
Stock Option to Buy
43.73
2021-02-24
2026-02-23
Common Stock
977.0
2933
D
Stock Option to Buy
66.32
2020-02-22
2027-02-21
Common Stock
1033.0
1033
D
Stock Option to Buy
66.32
2021-02-22
2027-02-21
Common Stock
1033.0
2066
D
Stock Option to Buy
66.32
2022-02-22
2027-02-21
Common Stock
1034.0
3100
D
Each restricted stock unit represents the right to receive, at settlement, one share of common stock.
One-third of these restricted stock units are scheduled to vest on each of February 27, 2020; February 27, 2021; and February 27, 2022.
One-third of these restricted stock units are scheduled to vest on each of February 28, 2019; February 28, 2020; and February 28, 2021.
Options shares granted from City Holding Company's 2013 Incentive Plan are subject to both time-based and performance-based vesting.
Victoria A. Faw, attorney-in-fact
2019-02-28