SUPPLEMENTAL INDENTURE NUMBER 3 Dated as of December 21, 2007

Exhibit 4.12

SUPPLEMENTAL INDENTURE NUMBER 3

Dated as of December 21, 2007

to

INDENTURE

Dated as of November 30, 1999

between

ACE INA HOLDINGS INC.,

as Issuer

and

THE BANK OF NEW YORK,

as Successor Trustee

SUPPLEMENTAL INDENTURE NUMBER 3

This SUPPLEMENTAL INDENTURE NUMBER 3, dated as of December 21, 2007, is made by and between ACE INA Holdings Inc., a Delaware corporation (the “Company”), and THE BANK OF NEW YORK, as successor trustee under the indenture referred to below (the “Trustee”).

WITNESSETH:

WHEREAS, the Company has heretofore executed and delivered to Bank One Trust Company, NA, as trustee, an Indenture, dated as of November 30, 1999, as amended by Supplemental Indenture Number 1 dated December 6, 1999 and Supplemental Indenture Number 2 and Waiver dated as of February 16, 2000 (as so amended, the “Indenture”) providing for the issuance of an aggregate principal amount of up to $300,000,000 of 11.20% Subordinated Notes due 2009 (the “Securities”);

WHEREAS, Bank One Trust Company, NA has transferred all or substantially all of its corporate trust business or assets to The Bank of New York and, pursuant to Section 7.09 of the Indenture, The Bank of New York has become the successor trustee;

WHEREAS, Section 104 of the aforementioned Supplemental Indenture No. 1 requires the Company to provide certain consolidated financial statements and other financial information to the Trustee and the Holders;

WHEREAS, Section 10.5 of the Indenture requires the Company to preserve the corporate existence of the Company and of each of its subsidiaries;

WHEREAS, the Company has requested, and the Trustee is prepared to agree, to amend Section 104 of Supplemental Indenture No. 1 and Section 10.5 of the Indenture as provided below (the “Amendment”);

WHEREAS, Holders of a majority in principal amount of the Securities have consented in writing to the Amendment; and

WHEREAS, pursuant to Section 9.2 of the Indenture, the Trustee and the Company are authorized to execute and deliver this Supplemental Indenture Number 3.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and the Trustee mutually covenant and agree for the equal and ratable benefit of the Securityholders as follows:

1. Amendments.

(a) Section 104 of Supplemental Indenture No.1 is hereby amended by deleting Section 104 in its entirety and replacing it with the following:

At any time while any Notes are Outstanding:

(a) within 120 days after the end of each fiscal year, the Company shall provide to the Trustee and Holders a Consolidated balance sheet of the Company and its Subsidiaries as of the end of such fiscal year and the related Consolidated statements of income, stockholders’ equity and cash flow of the Company and its Subsidiaries for such fiscal year, setting forth in each case in comparative form the Consolidated figures for the previous fiscal year, all in reasonable detail and accompanied by (i) a report thereon of independent certified public accountants of recognized national standing selected by the Company stating that such Consolidated financial statements fairly present the Consolidated financial position of the Company and its Subsidiaries as of the date indicated and their results of operations and cash flows for the periods indicated in conformity with GAAP (except as otherwise stated therein) and that the examination by such accountants in connection with such Consolidated financial statements has been made in accordance with generally accepted auditing standards and (ii) a management’s discussion and analysis of financial condition and results of operations substantially as would be required to be included in an annual report on Form 10-K if the Company were subject to the reporting requirements of Section 13 or 15(d) of the Exchange Act; provided that, the Company’s obligations under this Section 4.02(a) shall be fully satisfied of the foregoing obligation if ACE Limited has filed with the Securities and Exchange Commission on or before such 120^th day its Annual Report on Form 10-K for such fiscal year containing an audited condensed consolidated balance sheet and statements of operations and cash flows for the Company in the footnotes to the financial statements of ACE Limited contained therein, and the Company shall have given notice of the public availability thereof to the Trustee on or before such 120^th day.

(b) within 45 days after the end of each fiscal quarter (other than the last fiscal quarter of any fiscal year) the Company shall provide to the Trustee and Holders an unaudited Consolidated balance sheet of the Company and its Subsidiaries as of the end of such quarter and the related unaudited Consolidated statements of income, stockholders’ equity and cash flow for such quarter and the portion of the fiscal year ended at the end of such quarter, setting forth in each case in comparative form the Consolidated figures for the corresponding periods of the prior fiscal year, all in reasonable detail and certified by the Company’s chief financial officer as fairly presenting the Consolidated financial condition of the Company and its Subsidiaries as of the dates indicated, and their Consolidated results of operations and cash flows for the periods indicated, in conformity with GAAP, subject to normal year-end adjustments and the absence of footnotes; provided that, the Company’s obligations under this Section 4.02(b) shall be fully satisfied of the foregoing obligation if ACE Limited has filed with the Securities and Exchange Commission on or before such 45^th day its Quarterly Report on Form 10-Q for such fiscal quarter containing an unaudited

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condensed consolidated balance sheet and statements of operations and cash flows for the Company in the footnotes to the financial statements of ACE Limited contained therein, and the Company shall have given notice of the public availability thereof to the Trustee on or before such 45^th day; and

(c) the Company shall furnish to the Holders and prospective investors, upon their request, the information required to be delivered pursuant to Rule 144A(d)(4) under the Securities Act.

(b) Section 10.5 of the Indenture is hereby amended by deleting Section 10.5 in its entirety and replacing it with the following:

Section 10.5 Corporate Existence.

Subject to Article 8, the Company shall do or cause to be done all things necessary to preserve and keep in full force and effect its respective corporate existence and that of each of its Subsidiaries and their respective rights (charter and statutory) and franchises; provided, however, that the foregoing shall not obligate the Company or any of its Subsidiaries to preserve its corporate existence (in the case of a Subsidiary of the Company only) or any such right or franchise if the Company or any such Subsidiary shall determine that the preservation thereof is no longer desirable in the conduct of its business or the business of such Subsidiary and that the loss thereof is not disadvantageous in any material respect to any Holder.

2. Ratification of Indenture; Supplemental Indentures Part of Indenture. Except as expressly amended hereby, the Indenture is in all respects ratified and confirmed and all the terms, conditions and provisions thereof shall remain in full force and effect. This Supplemental Indenture Number 3 shall form a part of the Indenture for all purposes, and every Securityholder heretofore or hereafter authenticated and delivered shall be bound hereby.

3. Indemnity. The Company shall indemnify the Trustee and its officers, directors, employees and agents against any and all loss, liability or expense (including reasonable attorneys’ fees and expenses) incurred by or in connection with the execution and delivery of this Supplemental Indenture Number 3 and the performance of their duties hereunder.

4. Defined Terms. Capitalized terms used herein without definition shall have the respective terms assigned such terms in the Indenture.

5. Governing Law. THIS SUPPLEMENTAL INDENTURE NUMBER 3 SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK (WITHOUT REGARD TO THE CHOICE OF LAW PROVISIONS THEREOF THAT WOULD REQUIRE THE APPLICATION OF ANY OTHER LAWS).

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6. Trustee Makes No Representation. The Trustee makes no representation as to the validity or sufficiency of this Supplemental Indenture Number 3.

7. Counterparts. The parties may sign any number of copies of this Supplemental Indenture Number 4. Each signed copy shall be an original, but all of them together represent the same agreement.

8. Effect of Headings. The Section headings herein are for convenience only and shall not effect the construction thereof.

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture Number 3 to be duly executed as of the date first above written.

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