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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-10-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001166126</issuerCik>
        <issuerName>J C PENNEY CO INC</issuerName>
        <issuerTradingSymbol>JCP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000904503</rptOwnerCik>
            <rptOwnerName>ROTH STEVEN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O VORNADO REALTY TRUST</rptOwnerStreet1>
            <rptOwnerStreet2>888 SEVENTH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Contract</value>
                <footnoteId id="F3"/>
                <footnoteId id="F4"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2012-10-08</value>
                <footnoteId id="F3"/>
                <footnoteId id="F4"/>
            </transactionDate>
            <deemedExecutionDate>
                <value>2012-10-08</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>0</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2010-10-07</value>
            </exerciseDate>
            <expirationDate>
                <value>2022-10-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4815990</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4815990</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By VSPS I L.L.C.</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Mr. Roth is a trustee and the Chairman of the Board of Trustees of Vornado Realty Trust (&quot;Vornado&quot;), which is the general partner of Vornado Realty L.P. (&quot;VRLP&quot;).  VRLP is the sole member of VNO Fashion LLC and VSPS I L.L.C. (&quot;VSPS&quot;).  VRLP is the controlling shareholder of Two Penn Plaza REIT, INC. (&quot;Two Penn Inc&quot;).  Two Penn Inc is the sole member of Two Penn Plaza REIT JP Fashion LLC (&quot;Two Penn LLC&quot;).  VRLP is also the sole member of CESC H Street LLC (&quot;CESC&quot;).  CESC is the controlling shareholder of H Street Building Corporation (&quot;H Street Corp&quot;).  H Street Corp is the sole member of H Street JP Fashion LLC.  VRLP is the sole shareholder of Vornado RTR, Inc. and Vornado RTR, Inc. is the sole shareholder fo PCJ I Inc.</footnote>
        <footnote id="F2">Mr. Roth was elected to the board of directors of the Issuer on February 9, 2011.  As a trustee of Vornado, Mr. Roth may be deemed to have a pecuniary interest in certain of the shares of the Issuer beneficially owned by Vornado.  Mr. Roth disclaims any beneficial ownership of securities of the Issuer.</footnote>
        <footnote id="F3">On October 7, 2010, VSPS entered into a share forward transaction with Deutsche Bank AG, London Branch (&quot;DB&quot;) (the &quot;Forward Transaction&quot;).  On October 8, 2012, VSPS and DB amended and restated the confirmation for the Forward Transaction,  pursuant to which DB has agreed to sell to VSPS, for settlement no later than October 8, 2022, 4,815,990 shares of Common Stock of J.C. Penney Company, Inc. (&quot;Common Shares&quot;) at a per share forward price determined based on a formula.  At any time during the term of the Forward Transaction, VSPS may accelerate settlement of the Forward Transaction, in whole or in part, upon one business day's prior notice to DB, and DB may accelerate settlement of the Forward Transaction, in whole or in part, (a) in the case of a credit downgrade of VSPS, upon one business day's prior notice to VSPS or (b) on October 8, 2014, or any one or two year anniversary thereof (as applicable), by twenty business days' prior notice.</footnote>
        <footnote id="F4">The Forward Transaction may be settled, at the election of VSPS, in cash or by delivery of Common Shares in exchange for payment by VSPS of the forward price per share.  VSPS has agreed with DB that, while the Forward Transaction is outstanding, VSPS and its affiliates will not own or otherwise have economic exposure to more than 15.4% of the Common Shares outstanding at such time.  The amendment and restatement of the confirmation for the Forward Transaction is a transaction described in Rule 16a-4(d) of the Securities Exchange Act of 1934.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Steven Roth</signatureName>
        <signatureDate>2012-10-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
