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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-02-28</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>2023-02-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>219</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>28620</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </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="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </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="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </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>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>472.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>472</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="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F7"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>215.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>215</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="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-02-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>219</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F8"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>219.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>44.43</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-03-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1309.0</value>
                    <footnoteId id="F9"/>
                </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="F10"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-02-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>600.0</value>
                    <footnoteId id="F10"/>
                </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="F11"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-02-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3100.0</value>
                    <footnoteId id="F11"/>
                </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">Each restricted stock unit represents the right to receive, at settlement, one share of common stock.</footnote>
        <footnote id="F3">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="F4">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="F5">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="F6">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="F7">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="F8">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="F9">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="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: 600 shares on each of 2/26/2018, 2/26/2019 and 2/26/2020.</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: 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>2023-03-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2023-02-28
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
2023-02-28
4
M
0
219
0
A
28620
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
Common Stock
472.0
472
D
Restricted Stock Unit
0.0
Common Stock
215.0
215
D
Restricted Stock Unit
0.0
2023-02-28
4
M
0
219
0
D
Common Stock
219.0
0
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.
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
2023-03-01