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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-04-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000732417</issuerCik>
        <issuerName>HILLS BANCORPORATION</issuerName>
        <issuerTradingSymbol>HBIA.PK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001561282</rptOwnerCik>
            <rptOwnerName>DeMaris Shari J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O HILLS BANCORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>131 MAIN STREET</rptOwnerStreet2>
            <rptOwnerCity>HILLS</rptOwnerCity>
            <rptOwnerState>IA</rptOwnerState>
            <rptOwnerZipCode>52235</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Treasurer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2244</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-04-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>750</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>83.50</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2994</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>708</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Held Thru Bank ESOP</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>69.0</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2017-10-09</value>
            </exerciseDate>
            <expirationDate>
                <value>2022-10-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1500.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes></footnotes>

    <remarks>Common stock held includes 500 shares of restricted stock which vest on November 1, 2017, 750 shares of restricted stock which vest on April 8, 2019 and 750 shares of restricted stock which vest on April 14, 2020.</remarks>

    <ownerSignature>
        <signatureName>/s/ Shari DeMaris</signatureName>
        <signatureDate>2015-04-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2015-04-14
0
0000732417
HILLS BANCORPORATION
HBIA.PK
0001561282
DeMaris Shari J
C/O HILLS BANCORPORATION
131 MAIN STREET
HILLS
IA
52235
0
1
0
0
Treasurer
Common Stock
2244
D
Common Stock
2015-04-14
4
A
0
750
83.50
A
2994
D
Common Stock
708
I
Held Thru Bank ESOP
Common Stock
69.0
2017-10-09
2022-10-09
Common Stock
1500.0
1500
D
Common stock held includes 500 shares of restricted stock which vest on November 1, 2017, 750 shares of restricted stock which vest on April 8, 2019 and 750 shares of restricted stock which vest on April 14, 2020.
/s/ Shari DeMaris
2015-04-17