The daughter of John Chancellor and Mary Jolliffe, a daughter of Lord Hylton, Chancellor was brought up in Somerset and educated at St Mary's School, Shaftesbury, a Roman Catholic boarding school for girls in Dorset, but left at sixteen to live in London, later describing her early years there as "quite wild". She became the partner of the poet Jock Scot (1952–2016), and in her early twenties had a daughter, Poppy, whilst still studying at the London Academy of Music and Dramatic Art. She separated from Scot a few years later. She got her first acting role on television playing Mercedes Page in Jupiter Moon, a BSkyB soap, then came a commercial for Boddingtons beer and a part in the film Four Weddings and a Funeral (1994), playing "Duckface" opposite Hugh Grant.

Chancellor had a prominent role in the series Kavanagh QC. She has also been noted for her work as Caroline Bingley in the 1995 BBC adaptation of Pride and Prejudice, and as Questular Rontok in The Hitchhiker's Guide to the Galaxy (2005). The same year, she joined the cast of the popular BBC One television drama series Spooks as a new regular character, Juliet Shaw. She has also appeared in The Vice, Karaoke, Cold Lazarus, The Dreamers, Tipping the Velvet and Fortysomething, and had a leading role in the satirical black comedy Suburban Shootout. In 2011, she took a supporting role in the BBC thriller serial The Hour, for which she was nominated for the British Academy Television Award for Best Supporting Actress.

In 1997, she received a Laurence Olivier Award for Best Actress in a Supporting Role nomination for her performance in Stanley and in 2013 an Olivier Award for Best Actress nomination for her part in Private Lives.