<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-09-30</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001027884</issuerCik><issuerName>CHICAGO BRIDGE &amp; IRON CO N V</issuerName>        <issuerTradingSymbol>CBI</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001224929</rptOwnerCik><rptOwnerName>JENNETT J CHARLES</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>1450 LAKE ROBBINS DRIVE</rptOwnerStreet1><rptOwnerStreet2>SUITE 400</rptOwnerStreet2><rptOwnerCity>THE WOODLANDS</rptOwnerCity><rptOwnerState>TX</rptOwnerState><rptOwnerZipCode>77380</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>Phantom Stock Unit</value><footnoteId id="F1" /></securityTitle><conversionOrExercisePrice><value>0</value></conversionOrExercisePrice><transactionDate><value>2003-09-30</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>20.07</value></transactionShares><transactionPricePerShare><value>27.16</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F2" /></exerciseDate><expirationDate><footnoteId id="F2" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>20.07</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>13647.359</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Acquired pursuant to the CB&amp;I Supervisory Board of Directors Fee Payment Plan.</footnote><footnote id="F2">Shares of Phantom stock are payable in common stock one year after the reporting person's retirement from the Supervisory Board of Directors Fee Payment Plan.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>J.Charles Jennett</signatureName><signatureDate>2003-10-01</signatureDate></ownerSignature></ownershipDocument>

