<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-09-12</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000046640</issuerCik><issuerName>HEINZ H J CO</issuerName>        <issuerTradingSymbol>HNZ</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001055097</rptOwnerCik><rptOwnerName>KENDLE CANDACE B</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>KENDLE INTERNATIONAL INC.</rptOwnerStreet1><rptOwnerStreet2>700 CAREW TOWER, 441 VINE STREET</rptOwnerStreet2><rptOwnerCity>CINCINNATI</rptOwnerCity><rptOwnerState>OH</rptOwnerState><rptOwnerZipCode>45202</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, $.25 Par Value</value><footnoteId id="F1" /><footnoteId id="F2" /></securityTitle><transactionDate><value>2003-09-12</value></transactionDate><deemedExecutionDate><value>2003-09-12</value></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionAmounts><transactionShares><value>1000</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>4402</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">2003 Directors Stock Award</footnote><footnote id="F2">Includes 302 shares held in the H. J. Heinz Company Stock Investor Services Plan as of September 12, 2003.</footnote></footnotes><ownerSignature><signatureName>Candace Kendle</signatureName><signatureDate>2003-09-15</signatureDate></ownerSignature></ownershipDocument>

