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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-02-26</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>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>235</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>25534</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2652</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>28186</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>560.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>560</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>690.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>690</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>696.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>696</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>235</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F7"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>235.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>472</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="F3"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F8"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>430.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>430</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F9"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>219.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>219</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>
                <footnoteId id="F10"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-03-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1309.0</value>
                    <footnoteId id="F10"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1309</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>
                <footnoteId id="F11"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-02-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>600.0</value>
                    <footnoteId id="F11"/>
                </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>66.32</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F12"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-02-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3100.0</value>
                    <footnoteId id="F12"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3100</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Shares were received for no consideration upon vesting of the restricted stock units and the satisfaction of a two-year holding period.</footnote>
        <footnote id="F2">Shares were received for no consideration upon satisfaction of performance criteria underlying the award of performance share units.</footnote>
        <footnote id="F3">Each restricted stock unit represents the right to receive, at settlement, one share of common stock.</footnote>
        <footnote id="F4">One-third of these restricted stock units are scheduled to vest on each of February 22, 2024; February 24, 2025; and February 22, 2026.</footnote>
        <footnote id="F5">One-third of these restricted stock units are scheduled to vest on each of February 23, 2023; February 23, 2024; and February 23, 2025.</footnote>
        <footnote id="F6">One-third of these restricted stock units are scheduled to vest on each of February 24, 2022; February 24, 2023; and February 24, 2024.</footnote>
        <footnote id="F7">One-third of these restricted stock units are scheduled to vest on each of February 26, 2021; February 26, 2022; and February 26, 2023.</footnote>
        <footnote id="F8">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="F9">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="F10">Options shares granted from City Holding Company's 2013 Incentive Plan are subject to both time-based and performance-based vesting. Options shares shall vest as follows: 807 shares on each of 3/26/2017,3/26/2018 and 3/26/2019.</footnote>
        <footnote id="F11">Options shares granted from City Holding Company's 2013 Incentive Plan are subject to both time-based and performance-based vesting. Options shares shall vest as follows: 600 shares on each of 2/26/2018, 2/26/2019 and 2/26/2020.</footnote>
        <footnote id="F12">Options shares granted from City Holding Company's 2013 Incentive Plan are subject to both time-based and performance-based vesting. Options shares shall vest as follows: 1,033 shares on each of 2/22/2020, 2/22/2021 and 1,034 shares on 2/22/2022.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Victoria A. Faw, attorney-in-fact</signatureName>
        <signatureDate>2023-02-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2023-02-26
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
2023-02-26
4
M
0
235
0
A
25534
D
Common Stock
2023-02-26
4
A
0
2652
0
A
28186
D
Restricted Stock Unit
Common Stock
560.0
560
D
Restricted Stock Unit
Common Stock
690.0
690
D
Restricted Stock Unit
0.0
Common Stock
696.0
696
D
Restricted Stock Unit
0.0
2023-02-26
4
M
0
235
0
D
Common Stock
235.0
472
D
Restricted Stock Unit
0.0
Common Stock
430.0
430
D
Restricted Stock Unit
0.0
Common Stock
219.0
219
D
Stock Option to Buy
44.43
2024-03-25
Common Stock
1309.0
1309
D
Stock Option to Buy
46.61
2025-02-25
Common Stock
600.0
600
D
Stock Option to Buy
66.32
2027-02-21
Common Stock
3100.0
3100
D
Shares were received for no consideration upon vesting of the restricted stock units and the satisfaction of a two-year holding period.
Shares were received for no consideration upon satisfaction of performance criteria underlying the award of performance share units.
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 22, 2024; February 24, 2025; and February 22, 2026.
One-third of these restricted stock units are scheduled to vest on each of February 23, 2023; February 23, 2024; and February 23, 2025.
One-third of these restricted stock units are scheduled to vest on each of February 24, 2022; February 24, 2023; and February 24, 2024.
One-third of these restricted stock units are scheduled to vest on each of February 26, 2021; February 26, 2022; and February 26, 2023.
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. Options shares shall vest as follows: 807 shares on each of 3/26/2017,3/26/2018 and 3/26/2019.
Options shares granted from City Holding Company's 2013 Incentive Plan are subject to both time-based and performance-based vesting. Options shares shall vest as follows: 600 shares on each of 2/26/2018, 2/26/2019 and 2/26/2020.
Options shares granted from City Holding Company's 2013 Incentive Plan are subject to both time-based and performance-based vesting. Options shares shall vest as follows: 1,033 shares on each of 2/22/2020, 2/22/2021 and 1,034 shares on 2/22/2022.
Victoria A. Faw, attorney-in-fact
2023-02-27