<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>
	<periodOfReport>2003-12-23</periodOfReport>
	<notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000036029</issuerCik>
        <issuerName>FIRST FINANCIAL BANKSHARES INC</issuerName>
        <issuerTradingSymbol>FFIN</issuerTradingSymbol>
	</issuer>
	<reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001243213</rptOwnerCik>
            <rptOwnerName>MURPHY KENNETH T</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>400 PINE STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ABILENE</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>796040701</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
			<isDirector>1</isDirector>
			<isOfficer>0</isOfficer>
			<isTenPercentOwner>0</isTenPercentOwner>
			<isOther>0</isOther>
		</reportingOwnerRelationship>
	</reportingOwner>
	<nonDerivativeTable>
		<nonDerivativeTransaction>
			<securityTitle>
				<value>Common Stock</value>
			</securityTitle>
			<transactionDate>
				<value>2003-12-23</value>
			</transactionDate>
			<deemedExecutionDate>
			</deemedExecutionDate>
			<transactionCoding>
				<transactionFormType>4</transactionFormType>
				<transactionCode>G</transactionCode>
				<equitySwapInvolved>0</equitySwapInvolved>
			</transactionCoding>
			<transactionAmounts>
				<transactionShares>
					<value>1000</value>
				</transactionShares>
				<transactionPricePerShare>
					<value>0</value>
				</transactionPricePerShare>
				<transactionAcquiredDisposedCode>
					<value>D</value>
				</transactionAcquiredDisposedCode>
			</transactionAmounts>
			<postTransactionAmounts>
				<sharesOwnedFollowingTransaction>
					<value>204680.00</value>
					<footnoteId id="F1"/>
				</sharesOwnedFollowingTransaction>
			</postTransactionAmounts>
			<ownershipNature>
				<directOrIndirectOwnership>
					<value>D</value>
				</directOrIndirectOwnership>
				<natureOfOwnership>
					<value/>
				</natureOfOwnership>
			</ownershipNature>
		</nonDerivativeTransaction>
	</nonDerivativeTable>
	<footnotes>
		<footnote id="F1">Amount has been adjusted for five for four stock split effective 6/2/2003</footnote>
	</footnotes>
	<remarks>
	</remarks>
	<ownerSignature>
		<signatureName>By: J. Bruce Hildebrand, Attorney in Fact for</signatureName>
		<signatureDate>2003-12-23</signatureDate>
	</ownerSignature>
</ownershipDocument>

