-----BEGIN PRIVACY-ENHANCED MESSAGE-----
Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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MIC-Info: RSA-MD5,RSA,
 PxIFVPhNVZBzAujdyhwJ+QPNVM3PSbgbIwu09QIgCdCRKxQo1DXgPAiSAv69rrBD
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<SEC-DOCUMENT>0001181431-04-028620.txt : 20040601
<SEC-HEADER>0001181431-04-028620.hdr.sgml : 20040601
<ACCEPTANCE-DATETIME>20040601151733
ACCESSION NUMBER:		0001181431-04-028620
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:			STUART GARY M
		CENTRAL INDEX KEY:			0001072520

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-11778
		FILM NUMBER:		04841114

	BUSINESS ADDRESS:	
		STREET 1:		UNION PACIFIC CORP
		STREET 2:		1416 DODGE ST
		CITY:			OMAHA
		STATE:			NE
		ZIP:			68179
		BUSINESS PHONE:		4022713825

	MAIL ADDRESS:	
		STREET 1:		UNION PACIFIC CORP
		STREET 2:		1416 DODGE ST
		CITY:			OMAHA
		STATE:			NE
		ZIP:			68179
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>rrd44081.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>0001072520</rptOwnerCik>
            <rptOwnerName>STUART GARY M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>26 ROWAYTON</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</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>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16409.873</value>
                </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>
    </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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