Chambers was born on 11 March 1964, in Doncaster, the daughter of John Chambers, a consultant obstetrician and gynaecologist, and his wife Noelle, née Strange. She attended St. Mary's School and her secondary education was at St Swithun's School, Winchester, Hampshire. She then trained at the Webber Douglas Academy of Dramatic Art in the 1980s, where she was a classmate of actor Ross Kemp.

From 1994 to 2007, she played the role of Alice Tinker in the BBC comedy The Vicar of Dibley. Chambers appeared in all 20 episodes and four Comic Relief specials until 2007. In 1998, Chambers won the British Comedy Award for Best Actress for her performance.

Chambers voiced the character of "Belle Stickleback" in two series of the animated TV programme Pond Life (1996 and 2000) and took the role of Helen Yardley in the TV series How Do You Want Me? (1998) and appeared in the film Notting Hill (1999), as Honey, the younger sister of Hugh Grant's character.

She was cast as Martha Thompson in Take a Girl Like You (2000), a made-for-TV drama based on the Kingsley Amis novel and a remake of the 1970 film. Chambers worked as a voice performer in the animated made-for-TV film The Wind in the Willows (1995) and provided the voice of Spotty for two episodes in the CBeebies series Little Robots (2003).

She was in theatre for about 10 years before her first break in television. She appeared in a number of stage productions including Tartuffe and Invisible Friends. In 2002, she toured with the Michael Frayn play, Benefactors, where she starred opposite Neil Pearson.

On 26 February 2018, BBC One aired The Vicar of Dibley episode "Love and Marriage" in Chambers' memory. In similar vein, on 11 March 2018 (what would've been Chambers' 54th birthday), Gold hosted a The Vicar of Dibley day in her memory.