Exhibit 10.31

THIRD AMENDMENT OF ACE USA SUPPLEMENTAL EMPLOYEE RETIREMENT SAVINGS PLAN

WHEREAS, ACE INA Holdings, Inc., a Delaware corporation (the “Corporation”), maintains the ACE USA Supplemental Employee Retirement Savings Plan (the “Plan”); and

WHEREAS, employer contributions are credited to Participant accounts under the Plan based on participation in one or more of the ACE USA tax-qualified plans; and

WHEREAS, the Corporation desires to amend the ACE USA Employee Retirement Savings Plan, the ACE USA Basic Employee Retirement Savings Plan, the ACE USA Puerto Rico Employee Retirement Savings Plan and the ACE USA Basic Puerto Rico Employee Retirement Savings Plan (“ACE USA Qualified Plans”) to require employment on the last day of the Plan Year change to be eligible to receive for that year’s employer contributions. The Corporation further desires to amend the ACE USA Qualified Plans to exclude participation of employees of certain employers (or eliminate certain employer contributions) and add a “Performance-Based Contribution” for the employees of ESIS;

WHEREAS, Plan contributions to credit are determined by participation in and eligibility for contributions under the appropriate ACE USA Qualified Plans;

NOW, THEREFORE, RESOLVED, that by virtue and in exercise of the amending power reserved to the Corporation under the Plan, the Plan shall be, and hereby is, amended effective January 1, 2007 as follows:

1. The last sentence of Section 3.2 of the Plan is amended to read: “Credits of the Supplemental Basic Plan Benefit to the Participant’s Supplemental Basic Plan Account pursuant to this subsection 3.2 shall be made at the same time that Employer contributions would otherwise have been credited to his accounts under the ACE USA Basic Employee Retirement Savings Plan or the ACE USA Basic Puerto Rico Employee Retirement Savings Plan, as applicable, provided the eligibility requirements for Employer contributions under either said plan have been satisfied.”

2. The last sentence of Section 4.3 of the Plan is amended to read: “Credits to the Participant’s Accounts pursuant to this subsection 4.3 shall be made at the same time that matching contributions would otherwise have been credited to his accounts under either the ACE USA Employee Retirement Savings Plan or the ACE USA Puerto Rico Employee Retirement Savings Plan, as applicable, provided the eligibility requirements for matching contributions under either said plan have been satisfied.”

3. The last sentence of Section 4.4 of the Plan is amended to read: “Credits to the Participant’s Accounts pursuant to this subsection 4.4 shall be made at the same time that discretionary matching contributions would otherwise have been credited to his accounts under either the ACE USA Employee Retirement Savings Plan or the ACE USA Puerto

Rico Employee Retirement Savings Plan, as applicable, provided the eligibility requirements for contributions under either said plan have been satisfied.”

4. A new Section 4.5 is added to the Plan which reads:

“Supplemental ESIS Performance-Based Contributions. For any Plan Year a Participant’s Supplemental ESIS Performance-Based Account shall be credited with an amount equal to the difference, if any, between (a) the ESIS Performance-Based Contributions that would have been contributed on behalf of the Participant for that Plan Year to the ACE USA Employee Retirement Savings Plan or under the ACE USA Puerto Rico Employee Retirement Savings Plan, as applicable, determined without regard to the limitations of sections 401(a)(17), 401(k)(3), 401(m), 402(g) or 415 of the Code, and (b) the amount of ESIS Performance-Based Contributions actually made to the ACE USA Employee Retirement Savings Plan or the ACE USA Puerto Rico Employee Retirement Savings Plan, as applicable, on behalf of the Participant. Credits to the Participant’s Accounts pursuant to this subsection 4.4 shall be made at the same time that discretionary matching contributions would otherwise have been credited to his accounts under either the ACE USA Employee Retirement Savings Plan or the ACE USA Puerto Rico Employee Retirement Savings Plan, as applicable, provided the eligibility requirements for contributions under either said plan have been satisfied.”