June 29, 1999

Banc of America Securities LLC
600 Montgomery Street
San Francisco, California 91444

Ladies and Gentlemen:

     1.   Introduction. This letter agreement (the "Letter Agreement") confirms
our agreement with you ("BAS") relating to the issuance and sale of ordinary
shares, par value $0.041666667 per share (the "Ordinary Shares"), of ACE
Limited, a Cayman Islands company limited by shares (the "Company"), and certain
related matters.

     2.   Underwriting. (a) The Company shall designate by written notice to BAS
one or more target dates (each, a "Targeted Purchase Date") during the 36-month
period following the date hereof and ending on June 30, 2002 (the "Underwriting
Period") for the issuance and sale (an "Underwriting") by BAS (and potentially
other underwriters as contemplated below) of a number of Ordinary Shares (the
"Offered Shares" with respect to such Underwriting) having an aggregate Public
Offering Price (as defined below) with respect to such Underwriting equal to or
less than the Underwriting Commitment (as defined below), and the Company agrees
that it shall designate Targeted Purchase Dates so that the aggregate offering
price for all Underwritings shall equal the Initial Underwriting Commitment (as
defined below). If Underwritings having an aggregate public offering price of at
least the Initial Underwriting Commitment have not been completed prior to the
60th day preceding the end of the Underwriting Period, BAS shall be entitled to
designate a Targeted Purchase Date for an Underwriting of Offered Shares having
an aggregate Public Offering Price equal to the Underwriting Commitment by
written notice to the Company, which Targeted Purchase Date shall not be later
than the last day of the Underwriting Period.

          "Underwriting Commitment" means the excess, if any, of (i)
     $400,000,000 (the "Initial Underwriting Commitment") over (ii) the


     aggregate Public Offering Price (as defined below) of all Ordinary Shares
     (including any Additional Shares purchased pursuant to Section 2(c) below)
     sold in any Underwriting that has been completed prior to such date.

     (b)  Prior to each Targeted Purchase Date, each of the Company and BAS will
cooperate with the other party and use its reasonable best efforts to market the
Offered Shares.  Once marketing is complete, each of the Company and the
Underwriter will use its reasonable best efforts to agree to the terms,
including without limitation any pricing terms, of a firm commitment
underwriting and upon such agreement, enter into a Firm Commitment Underwriting
Agreement (the "Firm Commitment Underwriting Agreement") with respect to such
Offered Shares, substantially in the form of the Underwriting Agreement attached
hereto, with such changes as are mutually agreed to by BAS and the Company to
reflect the terms of the firm commitment underwriting and changed circumstances
and practices; provided that (i) so long as Offerings are consummated hereunder
during the Underwriting Period for an aggregate Public Offering Price at least
equal to the Initial Underwriting Commitment, the Company shall be under no
obligation to accept the proposed terms of any particular Offering and (ii) the
Company may designate additional underwriters, as provided for below.
Notwithstanding anything herein to the contrary, either the Company or BAS may
decline to enter into such Firm Commitment Underwriting Agreement if it believes
that doing so might result in any violation of applicable law or regulation.

     (c)  In the Firm Commitment Underwriting Agreement with respect to any
Underwriting, the Company will grant to the underwriters in such Firm Commitment
Underwriting Agreement the right to purchase at the Purchase Price (as defined
below) a number of additional Ordinary Shares (the "Additional Shares") not to
exceed 15% of the Offered Shares to be sold in such Underwriting.

     (d)  Subject to Section 2(e) below, the purchase price per Offered Share
(the "Purchase Price") to be paid by BAS to the Company pursuant to any Firm
Commitment Underwriting Agreement shall be equal to 97.50% of the price at which
each Offered Share is initially to be offered to the public (the "Public
Offering Price").

     (e)  The parties contemplate that any Underwritings hereunder will be
solely underwritten by BAS. The Company may elect to include another broker-
dealer as a joint book-running manager together with BAS in any Underwriting
hereunder and one or more co-managing underwriters; provided that in such event,
the Purchase Price in such Underwriting shall be equal to 97.0% of the

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Public Offering Price, and BAS shall be entitled to at least 50% of any
applicable management fees, underwriting discounts and commissions (1.50% of the
Public Offering Price); provided further that BAS shall be entitled to at least
25% of such fees, discounts and commissions (0.75% of the Public Offering Price)
if, in the reasonable judgment of the Company prior to the marketing of such
offering, BAS is unable to meet the standards of other nationally recognized
investment banks in connection with such Underwriting, it being understood that
BAS shall be deemed to be unable to meet the standards of other nationally
recognized investment banks in connection with such an Underwriting only if a
significant decline in BAS's current equity distribution capabilities occurs.

     3.   Shelf Registration. The Company has prepared and filed with the
Securities and Exchange Commission a registration statement on Form S-3
("Registration Statement") relating to the offer and sale of Ordinary Shares and
other securities, with a proposed aggregate public offering price equal to
$4,000,000,000, on a continuous or delayed basis pursuant to Rule 415 under the
Securities Act of 1933, as amended (the "1933 Act").  The Company shall use its
reasonable best efforts to (i) if necessary, cause the Registration Statement to
become effective under the 1933 Act as soon as practicable after such filing and
(ii) keep the Registration Statement effective with unused capacity at least
equal to 115% of the Underwriting Commitment until the conclusion of the
Underwriting Period.

     4.   Termination. This Letter Agreement will terminate on the earliest of
(i) the date on which the underwritings contemplated hereby are completed, (ii)
the last day of the Underwriting Period and (iii) July 9, 1999 if the closing
under the Placement Agreement dated as of June 29, 1999 among the Company, ACE
INA Holdings Inc., a Delaware corporation, ACE RHINOS Trust, a Delaware business
trust, and Intrepid Funding Master Trust, a Delaware business trust, has not
occurred.

     5.   Expenses. Except as otherwise provided in each Firm Commitment
Underwriting Agreement, all costs and expenses (including any fees,
disbursements and expenses of counsel) incurred in connection with this Letter
Agreement and the Underwritings contemplated hereby shall be paid by the party
incurring such expenses; provided that if the underwritings contemplated hereby
are not completed prior to conclusion of the Underwriting Period, the Company
will pay all such expenses incurred by BAS or any of its affiliates.

     6.   Governing Law. This Letter Agreement shall be governed by and
construed in accordance with the substantive law of the State of New York.

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     7.   Binding Obligation; Reasonable Best Efforts. It is understood that
this Letter Agreement constitutes a legally binding obligation of the parties
hereto. The parties agree to use their reasonable best efforts to take, or cause
to be taken, all actions and to do, or cause to be done, all things necessary to
consummate the transactions contemplated by this Letter Agreement.

     8.   Counterparts. This Letter Agreement may be signed in any number of
counterparts, each of which shall be an original, with the same effect as if the
signatures thereto and hereto were upon the same instrument.

     9.   Purchase for Resale. BAS confirms its intention that any Ordinary
Shares purchased by it pursuant to this Letter Agreement will be purchased for
resale to third parties pursuant to a bona fide public offering.

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     Please confirm your agreement with the foregoing by signing and returning a
copy of this Letter Agreement to the undersigned.


                                        Very truly yours,

                                        ACE LIMITED


                                        By:____________________________________
                                           Name: Peter N. Mear
                                           Title: Secretary


Accepted and Agreed as of
the date first above written:

BANC OF AMERICA SECURITIES LLC


By:____________________________
   Name: Trevor Ganshaw
   Title: Managing Director