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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-02-28</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>

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            </securityTitle>
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                </sharesOwnedFollowingTransaction>
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                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>219</value>
                </transactionShares>
                <transactionPricePerShare>
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                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionAcquiredDisposedCode>
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                <footnoteId id="F7"/>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
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                </sharesOwnedFollowingTransaction>
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        <derivativeHolding>
            <securityTitle>
                <value>Stock Option to Buy</value>
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            <exerciseDate>
                <value>2018-02-27</value>
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            <expirationDate>
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            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
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            <underlyingSecurity>
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            <ownershipNature>
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                    <footnoteId id="F8"/>
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                <underlyingSecurityTitle>
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                <underlyingSecurityShares>
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                    <footnoteId id="F8"/>
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                <directOrIndirectOwnership>
                    <value>D</value>
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                    <footnoteId id="F8"/>
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            <ownershipNature>
                <directOrIndirectOwnership>
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                    <footnoteId id="F8"/>
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                    <footnoteId id="F8"/>
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    </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 24, 2022; February 24, 2023; and February 24, 2024.</footnote>
        <footnote id="F5">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="F6">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="F7">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="F8">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>2021-03-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2021-02-28
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
20972
D
Common Stock
2021-02-28
4
M
0
219
0
A
21191
D
Common Stock
2021-02-28
4
A
0
2415
0
A
23606
D
Restricted Stock Unit
0.0
2021-02-28
4
A
0
0
0
A
Common Stock
0.0
696
D
Restricted Stock Unit
0.0
Common Stock
707.0
707
D
Restricted Stock Unit
0.0
Common Stock
645.0
645
D
Restricted Stock Unit
0.0
2021-02-28
4
M
0
219
0
D
Common Stock
219.0
438
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
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 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.
Victoria A. Faw, attorney-in-fact
2021-03-02