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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-01-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001631569</issuerCik>
        <issuerName>Community Healthcare Trust Inc</issuerName>
        <issuerTradingSymbol>CHCT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001210485</rptOwnerCik>
            <rptOwnerName>WALLACE TIMOTHY G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O COMMUNITY HEALTHCARE TRUST INCORPORA</rptOwnerStreet1>
            <rptOwnerStreet2>3326 ASPEN GROVE DRIVE, SUITE 150</rptOwnerStreet2>
            <rptOwnerCity>FRANKLIN</rptOwnerCity>
            <rptOwnerState>TN</rptOwnerState>
            <rptOwnerZipCode>37067</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman, CEO and President</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-01-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>32651</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.05</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>384326</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>120000</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote (2)</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">For 2017, the reporting person agreed to take 100% of his salary in the form of shares of restricted stock with an eight-year restriction period.  Because the reporting person elected to take his base salary for 2017 in these shares of restricted stock, the Company awarded Mr. Wallace additional compensation, in restricted stock, equal to his annual salary. The price of the securities acquired by the reporting person is based on the volume weighted average price of the Company's common stock for the 10 trading days immediately preceding January 13, 2017, which was $23.05.  The number of securities issued is equal to the total salary, including the additional compensation, divided by such price.</footnote>
        <footnote id="F2">The amount shown represents the beneficial ownership of the Company's securities by Athena Funding Partners, LLC (&quot;AFP&quot;).  The reporting person owns 99% of AFP and disclaims beneficial ownership of the securities to the extent it exceeds his pecuniary interest therein and the inclusion of the shares in this report shall not be deemed to be an admission of beneficial ownership of the reported shares for the purposes of Section 16 of the Exchange Act or otherwise.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Christopher M. Douse, Attorney-in-Fact</signatureName>
        <signatureDate>2017-01-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
