Clients of Chubb consist of multinational corporations and local businesses, individuals, and insurers seeking reinsurance coverage.

[5] Its core operating insurance companies are rated "AA" (Very Strong) for financial strength by Standard & Poor's[6][7] and "A++" (Superior) by A. M. Best[8][9] with stable outlooks from both agencies.

Fitch rates Chubb Limited and its subsidiaries "AA" (Very Strong) for financial strength, "AA−" for issuer default and "A+" for senior debt.

In 1987 the company assumed management of Corporate Officers & Directors Assurance Limited (CODA), expanding ACE Bermuda's product line.

[19] One of the multiple acquisitions made during this time was the global property and casualty business of Cigna Corporation (most significantly the Insurance Company of North America, known as INA), which was purchased for $3.45 billion in 1999.

Evan Greenberg described the move as a "natural progression" that would provide ACE with a "better strategic flexibility…and a solid legal and regulatory environment…"[26] The re-domestication was completed in July that year.

[27] In 2010, the ACE company ESIS Inc. was hired by BP to process claims made by the victims of the Deepwater Horizon oil spill.

[38] In October 2014, ACE Limited acquired the large commercial property and casualty business of Itaú Unibanco Holding SA.

[39] In April 2015, ACE Limited acquired the Fireman's Fund high net-worth personal lines insurance business in the U.S. from Allianz for $365 million.

[41] In February 2021, Chubb Limited and the World Health Organization announced the roll out of a no-fault compensation scheme for COVID-19 vaccinations for low and middle-income countries.

[47][48] As part of an $80 million settlement that abated further inquiry, ACE signed an Assurance of Discontinuance in which they acknowledged their prior conduct and agreed to alter their business practices.

[53][54] Despite an estimated net worth of over $2 billion,[55] Trump needed a cash bond posted by Chubb in order to secure his appeal.

While President, Trump appointed Chubb CEO Evan G. Greenberg to the White House advisory committee for trade policy and negotiations.