Maxwell was educated at Melbourne Grammar School and the University of Melbourne where he was resident at Trinity College. He played rugby and Australian rules football at Trinity, where he was the senior student in 1973. After graduating with honours in 1974, he was selected as Victorian Rhodes Scholar for 1975, completing a Bachelor of Philosophy at Oxford University. In 1978, he became a barrister at Lincoln's Inn in London practising briefly at the English Bar. In 1979, he returned to Melbourne working as a solicitor at law firm Phillips Fox. In 1981, he became principal private secretary to ALP Senator Gareth Evans who was appointed as federal Attorney-General in 1983. In 1983, he left to become a barrister in Victoria and was variously reader for Kenneth Hayne QC and reader for Ross Robson QC. He signed the Victorian Bar Roll in 1984 and became a QC in 1998.
Maxwell was a Victorian Legal Aid Commissioner for seven years from 1986 and also a member of the board of Liberty Victoria for six years, two of them as president from 2000. He appeared with Julian Burnside QC in the Tampa refugee case, and was then famously but unsuccessfully countersued (as a board member of Liberty Victoria) by the Commonwealth of Australia for costs. In 1982 he published An Introduction to the Securities Industry Codes (Sydney: Butterworths, 1982) with Robert Baxt and Selwyn Bajada, released in a second edition in 1988 as Stock Markets and the Securities industry: Law and Practice (Sydney: Butterworths, 1988). In 2002, he was later commissioned by the Victorian government to review the Occupational Health and Safety Act 1985.
In 2019, Maxwell heard the high profile County Court appeal of Cardinal George Pell against his conviction for the commission of sexual offences. Maxwell concurred with the Court of Appeal 2-1 majority rejecting the appeal, which was subsequently overruled by the High Court.
- "Queen's birthday honours". Sydney Morning Herald. 8 June 2015.
- Law Institute of Victoria (2005). "Maxwell's House". Law Institute Journal. 79 (9): 18. Retrieved 22 April 2020.
- "Meet our Alumni - The Hon Christopher Murray Maxwell OM 1970". Melbourne Grammar School. 2008. Retrieved 22 April 2020.
- "Leo Cussen Justice Speech 2016". La Trobe University Law Students' Association. Retrieved 22 April 2020.
- Maxwell, Chris (March 2004). Occupational Health and Safety Act Review (PDF). State of Victoria. ISBN 1920921044. Archived from the original (PDF) on 1 September 2007.
- "George Pell Victorian Court of Appeal judgment summary transcript". ABC News. 21 August 2019. Retrieved 23 April 2020.
- "Judgement Summary: Pell v The Queen  HCA 12" (PDF). High Court of Australia. 7 April 2020. Retrieved 23 April 2020.