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

    <schemaVersion>X0203</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2010-01-06</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001328650</issuerCik>
        <issuerName>Bronco Drilling Company, Inc.</issuerName>
        <issuerTradingSymbol>BRNC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001480249</rptOwnerCik>
            <rptOwnerName>Porter Matthew S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BRONCO DRILLING COMPANY INC.</rptOwnerStreet1>
            <rptOwnerStreet2>16217 NORTH MAY AVENUE</rptOwnerStreet2>
            <rptOwnerCity>EDMOND</rptOwnerCity>
            <rptOwnerState>OK</rptOwnerState>
            <rptOwnerZipCode>73013</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle>Chief Financial Officer</officerTitle>
            <otherText>Treasurer and Secretary</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15000</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Shares of restricted stock previously issued to the reporting person under the Bronco Drilling Company, Inc. 2006 Equity Incentive Plan.  Of these shares, 10,000 will vest on February 25, 2010, and 5,000 will vest on February 25, 2011.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Matthew S. Porter</signatureName>
        <signatureDate>2010-01-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
