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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-06-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001188873</rptOwnerCik>
            <rptOwnerName>LUMSDAINE ALFRED</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>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-06-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2726</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>19.079</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14777</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">For 2016, the reporting person elected to take 100% of their Board retainer in the form of shares of restricted stock with a three-year restriction period.  Because the reporting person elected to take their Board retainer for 2016 in these shares of restricted stock in lieu of cash, the Company awarded them additional shares of restricted stock, equal to 60% of their Board retainer.  The price of the securities acquired by the reporting person with respect to the Board retainer is based upon the ten (10) day average stock price of our common stock, which is equal to $19.079. The number of securities issued is equal to the total Board retainer, including the additional shares, divided by such 10-day average stock price.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Christopher M. Douse, Attorney-in-Fact</signatureName>
        <signatureDate>2016-06-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
