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Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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MIC-Info: RSA-MD5,RSA,
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<SEC-DOCUMENT>0001181431-04-028628.txt : 20040601
<SEC-HEADER>0001181431-04-028628.hdr.sgml : 20040601
<ACCEPTANCE-DATETIME>20040601151954
ACCESSION NUMBER:		0001181431-04-028628
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20040527
FILED AS OF DATE:		20040601

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			ACE LTD
		CENTRAL INDEX KEY:			0000896159
		STANDARD INDUSTRIAL CLASSIFICATION:	FIRE, MARINE & CASUALTY INSURANCE [6331]
		IRS NUMBER:				000000000
		STATE OF INCORPORATION:			D0
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		ACE BLDG
		STREET 2:		30 WOODBOURNE AVE
		CITY:			HAMILTON HM 08 BERMU
		STATE:			D0
		ZIP:			00000
		BUSINESS PHONE:		8092955200

	MAIL ADDRESS:	
		STREET 1:		P O BOX HM 1015
		CITY:			HAMITON BERMUDA
		STATE:			D0
		ZIP:			00000

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			HERNANDEZ ROBERT M
		CENTRAL INDEX KEY:			0001072509

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-11778
		FILM NUMBER:		04841136

	BUSINESS ADDRESS:	
		STREET 1:		USX CORP
		STREET 2:		600 GRANT ST ROOM 6105
		CITY:			PITTSBURGH
		STATE:			PA
		ZIP:			15219-4776
		BUSINESS PHONE:		4124331137

	MAIL ADDRESS:	
		STREET 1:		USX CORP
		STREET 2:		600 GRANT ST ROOM 6105
		CITY:			NEW YORK
		STATE:			NY
		ZIP:			10260
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>rrd44075.xml
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-05-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000896159</issuerCik>
        <issuerName>ACE LTD</issuerName>
        <issuerTradingSymbol>ACE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001072509</rptOwnerCik>
            <rptOwnerName>HERNANDEZ ROBERT M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1726 DENNISTON STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PITTSBURGH</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>15217-1715</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2004-05-27</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2168.675</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>41.50</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12987.362</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Stock units, representing the right to receive Ordinary Shares, granted as an annual director retainer fee issued under the ACE Limited 2004 Long-Term Incentive Plan (the &quot;Plan&quot;), which meets the requirements of Rule 16b-3.  Such stock units will vest on the day prior to the date of the next annual ACE Limited shareholder meeting, assuming the reporting person is a director of ACE Limited on such date.  Ordinary Shares will be issued for such stock units six months after the Director's termination from the Board or pursuant to such later deferral schedule as the director may elect.</footnote>
        <footnote id="F2">In addition, reporting person indirectly owns 38,001 Ordinary Shares held by a trust.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>By: Peter N. Mear  Attorney-in-fact</signatureName>
        <signatureDate>2004-06-01</signatureDate>
    </ownerSignature>
</ownershipDocument>

</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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