ACE LIMITED 1998 LONG-TERM INCENTIVE PLAN (As Amended Through the Fourth Amendment thereof,effective November 16, 2006) SECTION 1 GENERAL

Exhibit 10.34

Conformed Copy

ACE LIMITED 1998

LONG-TERM INCENTIVE PLAN

(As Amended Through the Fourth Amendment thereof, effective November 16, 2006)

SECTION 1

GENERAL

1.1. Purpose. The ACE Limited Long-Term Incentive Plan (the “Plan”) has been established by ACE Limited (the “Company”) to (i) attract and retain persons eligible to participate in the Plan; (ii) motivate Participants, by means of appropriate incentives, to achieve long-range goals; (iii) provide incentive compensation opportunities that are competitive with those of other similar companies; and (iv) further identify Participants’ interests with those of the Company’s other shareholders through compensation that is based on the Company’s ordinary shares of stock; and thereby promote the long-term financial interest of the Company and the Subsidiaries, including the growth in value of the Company’s equity and enhancement of long-term shareholder return.

1.2. Participation. Subject to the terms and conditions of the Plan, the Committee shall determine and designate, from time to time, from among the Eligible Individuals (including transferees of Eligible Individuals to the extent the transfer is permitted by the Plan and the applicable Award Agreement), those persons who will be granted one or more Awards under the Plan, and thereby become “Participants” in the Plan. In the discretion of the Committee, a Participant may be granted any Award permitted under the provisions of the Plan, and more than one Award may be granted to a Participant. Awards may be granted as alternatives to or replacement of awards granted or outstanding under the Plan, or any other plan or arrangement of the Company or a Subsidiary (including a plan or arrangement of a business or entity, all or a portion of which is acquired by the Company or a Subsidiary).

1.3. Operation, Administration, and Definitions. The operation and administration of the Plan, including the Awards made under the Plan, shall be subject to the provisions of Section 4 (relating to operation and administration). Capitalized terms in the Plan shall be defined as set forth in the Plan (including the definition provisions of Section 8 of the Plan).

SECTION 2

OPTIONS AND SARS

2.1. Definitions.

2.2. Exercise Price. The “Exercise Price” of each Option and SAR granted under this Section 2 shall be established by the Committee or shall be determined by a method established by the Committee at the time the Option or SAR is granted; except that the Exercise Price shall not be less than 100% of the Fair Market Value of a share of Stock on the date of grant (or, if greater, the par value of a share of Stock).

2.3. Exercise. An Option and an SAR shall be exercisable in accordance with such terms and conditions and during such periods as may be established by the Committee.

2.4. Payment of Option Exercise Price. The payment of the Exercise Price of an Option granted under this Section 2 shall be subject to the following:

2.5. Settlement of Award. Shares of Stock delivered pursuant to the exercise of an Option or SAR shall be subject to such conditions, restrictions and contingencies as the Committee may establish in the applicable Award Agreement. Settlement of SARs may be made in shares of Stock (valued at their Fair Market Value at the time of exercise), in cash, or in a combination thereof, as determined in the discretion of the Committee. The Committee, in its discretion, may impose such conditions, restrictions and contingencies with respect to shares of Stock acquired pursuant to the exercise of an Option or an SAR as the Committee determines to be desirable.

-2-

SECTION 3

OTHER STOCK AWARDS

3.1. Definitions.

3.2. Restrictions on Awards. Each Stock Unit Award, Restricted Stock Award, Restricted Stock Unit Award, Performance Share Award and Performance Unit Award shall be subject to the following:

-3-

SECTION 4

OPERATION AND ADMINISTRATION

4.1. Effective Date. Subject to the approval of the shareholders of the Company at the Company’s 1999 annual meeting of its shareholders, the Plan shall be effective as of November 13, 1998 (the “Effective Date”); provided, however, that to the extent that Awards are granted under the Plan prior to its approval by shareholders, the Awards shall be contingent on approval of the Plan by the shareholders of the Company at such annual meeting. The Plan shall be unlimited in duration and, in the event of Plan termination, shall remain in effect as long as any Awards under it are outstanding; provided, however, that no Awards may be granted under the Plan after the ten-year anniversary of the Effective Date.

4.2. Shares Subject to Plan. The shares of Stock for which Awards may be granted under the Plan shall be subject to the following:

-4-

(i) The maximum number of shares of Stock that may be issued by Options intended to be ISOs shall be 8,000,000 shares.

(ii) The maximum number of shares that may be covered by Awards granted to any one individual pursuant to Section 2 (relating to Options and SARs) shall be 6,000,000 shares during any one-calendar-year period.

(iii) The maximum number of shares of Stock that may be issued in conjunction with Awards granted pursuant to Section 3 (relating to Other Stock Awards) shall equal the sum of 2,500,000 shares plus the number of shares of Stock subject to Awards granted in replacement of awards given up by persons who became employed by the Company and the Subsidiaries in connection with the acquisition described in the acquisition agreement dated as of January 11, 1999 by and among the Company, CIGNA Corporation, and CIGNA Holdings, Inc.

(iv) For Stock Unit Awards, Restricted Stock Awards, Restricted Stock Unit Awards and Performance Share Awards that are intended to be “performance-based compensation” (as that term is used for purposes of Code section 162(m)), no more than 2,000,000 shares of Stock may be subject to such Awards granted to any one individual during any one-calendar-year period (regardless of when such shares are deliverable).

(v) For Performance Unit Awards that are intended to be “performance-based compensation” (as that term is used for purposes of Code section 162(m)), no more than $5,000,000 may be subject to such Awards granted to any one individual during any one-calendar-year period (regardless of when such amounts are deliverable).

-5-

4.3. General Restrictions. Delivery of shares of Stock or other amounts under the Plan shall be subject to the following:

4.4. Tax Withholding. All distributions under the Plan are subject to withholding of all applicable taxes, and the Committee may condition the delivery of any shares or other benefits under the Plan on satisfaction of the applicable withholding obligations. Except as otherwise provided by the Committee, such withholding obligations may be satisfied (i) through cash payment by the Participant, (ii) through the surrender of shares of Stock which the Participant already owns, or (iii) through the surrender of shares of Stock to which the Participant is otherwise entitled under the Plan; provided, however, that such shares under this clause (iii) may be used to satisfy not more than the Company’s minimum statutory withholding obligation (based on minimum statutory withholding rates for Federal and state tax purposes, including payroll taxes, that are applicable to such supplemental taxable income).

4.5. Use of Shares. Subject to the overall limitation on the number of shares of Stock that may be delivered under the Plan, the Committee may use available shares of Stock as the form of payment for compensation, grants or rights earned or due under any other compensation plans or arrangements of the Company or a Subsidiary, including the plans and arrangements of the Company or a Subsidiary assumed in business combinations.

4.6. Dividends and Dividend Equivalents. An Award (including without limitation an Option or SAR Award) may provide the Participant with the right to receive dividend payments or dividend equivalent payments with respect to Stock subject to the Award (both before and after the Stock subject to the Award is earned, vested, or acquired), which payments may be either made currently or credited to an account for the Participant, and may be settled in cash or Stock as determined by the Committee. Any such settlements, and any such crediting of dividends or dividend equivalents or reinvestment in shares of Stock, may be subject to such

-6-

conditions, restrictions and contingencies as the Committee shall establish, including the reinvestment of such credited amounts in Stock equivalents.

4.7. Payments. Awards may be settled through cash payments, the delivery of shares of Stock, the granting of replacement Awards, or combination thereof as the Committee shall determine. Any Award settlement, including payment deferrals, may be subject to such conditions, restrictions and contingencies as the Committee shall determine. The Committee may permit or require the deferral of any Award payment, subject to such rules and procedures as it may establish, which may include provisions for the payment or crediting of interest, or dividend equivalents, including converting such credits into deferred Stock equivalents. Each Subsidiary shall be liable for payment of cash due under the Plan with respect to any Participant to the extent that such benefits are attributable to the services rendered for that Subsidiary by the Participant. Any disputes relating to liability of a Subsidiary for cash payments shall be resolved by the Committee.

4.8. Transferability. Except as otherwise provided by the Committee, Awards under the Plan are not transferable except as designated by the Participant by will or by the laws of descent and distribution.

4.9. Form and Time of Elections. Unless otherwise specified herein, each election required or permitted to be made by any Participant or other person entitled to benefits under the Plan, and any permitted modification, or revocation thereof, shall be in writing filed with the Committee at such times, in such form, and subject to such restrictions and limitations, not inconsistent with the terms of the Plan, as the Committee shall require.

4.10. Agreement With Company. An Award under the Plan shall be subject to such terms and conditions, not inconsistent with the Plan, as the Committee shall, in its sole discretion, prescribe. The terms and conditions of any Award to any Participant shall be reflected in such form of written document as is determined by the Committee. A copy of such document shall be provided to the Participant, and the Committee may, but need not require that the Participant sign a copy of such document. Such document is referred to in the Plan as an “Award Agreement” regardless of whether any Participant signature is required.

4.11. Action by Company or Subsidiary. Any action required or permitted to be taken by the Company or any Subsidiary shall be by resolution of its board of directors, or by action of one or more members of the board (including a committee of the board) who are duly authorized to act for the board, or (except to the extent prohibited by applicable law or applicable rules of any stock exchange) by a duly authorized officer of such company.

4.12. Gender and Number. Where the context admits, words in any gender shall include any other gender, words in the singular shall include the plural and the plural shall include the singular.

4.13. Limitation of Implied Rights.

-7-

4.14. Benefits Under Qualified Retirement Plans. Except as otherwise provided by the Committee, Awards to a Participant (including the grant and the receipt of benefits) under the Plan shall be disregarded for purposes of determining the Participant’s benefits under any Qualified Retirement Plan and other plans maintained by the Participant’s employer. The term “Qualified Retirement Plan” means any plan of the Company or a Subsidiary that is intended to be qualified under section 401(a) of the Code.

4.15. Evidence. Evidence required of anyone under the Plan may be by certificate, affidavit, document or other information which the person acting on it considers pertinent and reliable, and signed, made or presented by the proper party or parties.

SECTION 5

CHANGE IN CONTROL

Subject to the provisions of paragraph 4.2(f) (relating to the adjustment of shares), and except as otherwise provided in the Plan or the Award Agreement reflecting the applicable Award, upon the occurrence of a Change in Control:

-8-

SECTION 6

COMMITTEE

6.1. Administration. The authority to control and manage the operation and administration of the Plan shall be vested in a committee (the “Committee”) in accordance with this Section 6. The Compensation Committee of the Board shall serve as the “Committee” under the Plan, except as otherwise determined by the Board. If the Committee does not exist, or for any other reason determined by the Board, the Board may take any action under the Plan that would otherwise be the responsibility of the Committee.

6.2. Powers of Committee. The Committee’s administration of the Plan shall be subject to the following:

6.3. Delegation by Committee. Except to the extent prohibited by applicable law or the applicable rules of a stock exchange, the Committee may allocate all or any portion of its responsibilities and powers to any one or more of its members and may delegate all or any part of its responsibilities and powers to any person or persons selected by it. Any such allocation or delegation may be revoked by the Committee at any time.

6.4. Information to be Furnished to Committee. The Company and Subsidiaries shall furnish the Committee with such data and information as it determines may be required for it to

-9-

discharge its duties. The records of the Company and Subsidiaries as to an employee’s or Participant’s employment (or other provision of services), termination of employment (or cessation of the provision of services), leave of absence, reemployment and compensation shall be conclusive on all persons unless determined to be incorrect. Participants and other persons entitled to benefits under the Plan must furnish the Committee such evidence, data or information as the Committee considers desirable to carry out the terms of the Plan.

SECTION 7

AMENDMENT AND TERMINATION

The Board may, at any time, amend or terminate the Plan, provided that no amendment or termination may, in the absence of written consent to the change by the affected Participant (or, if the Participant is not then living, the affected beneficiary), adversely affect the rights of any Participant or beneficiary under any Award granted under the Plan prior to the date such amendment is adopted by the Board; provided that adjustments pursuant to subject to paragraph 4.2(f) shall not be subject to the foregoing limitations of this Section 7.

SECTION 8

DEFINED TERMS

In addition to the other definitions contained herein, the following definitions shall apply:

(i) any “person,” as such term is used in Sections 3(a)(9) and 13(d) of the United States Securities Exchange Act of 1934, becomes a “beneficial owner,” as such term is used in Rule 13d-3 promulgated under that act, of 50% or more of the Voting Stock (as defined below) of the Company;

(ii) the majority of the Board consists of individuals other than Incumbent Directors, which term means the members of the Board on the Effective Date; provided that any person becoming a director subsequent to such date whose election or nomination for election was supported by three-quarters of the directors who then comprised the Incumbent Directors shall be considered to be an Incumbent Director;

(iii) the Company adopts any plan of liquidation providing for the distribution of all or substantially all of its assets;

-10-

(iv) all or substantially all of the assets or business of the Company is disposed of pursuant to a merger, consolidation or other transaction (unless the shareholders of the Company immediately prior to such merger, consolidation or other transaction beneficially own, directly or indirectly, in substantially the same proportion as they owned the Voting Stock of the Company, all of the Voting Stock or other ownership interests of the entity or entities, if any, that succeed to the business of the Company); or

(v) the Company combines with another company and is the surviving corporation but, immediately after the combination, the shareholders of the Company immediately prior to the combination hold, directly or indirectly, 50% or less of the Voting Stock of the combined company (there being excluded from the number of shares held by such shareholders, but not from the Voting Stock of the combined company, any shares received by Affiliates (as defined below) of such other company in exchange for stock of such other company).

For the purpose of this definition of “Change in Control,” (I) an “Affiliate” of a person or other entity shall mean a person or other entity that directly or indirectly controls, is controlled by, or is under common control with the person or other entity specified and (II) “Voting Stock” shall mean capital stock of any class or classes having general voting power under ordinary circumstances, in the absence of contingencies, to elect the directors of a corporation.

-11-

-12-