Born on 2 June 1961 in Greenwich, London, England in the United Kingdom, Chapman was abandoned by his father as a child and brought up by his mother. He admits that he was not particularly interested in school, except for English and Drama and, aged 14, moved to stage school, from where he gained early experience in film and television. At the age of 17 he met the Director Alan Clarke, who cast him in his film about Borstal life, Scum. He has since played a variety of roles in British theatre and in both British and European cinema.

His repertory work outside London during the 1980s includes Hamlet (Royal Exchange),Pride and Prejudice (Leicester Haymarket), The Clandestine Marriage (Bristol, Old Vic), Comedy of Errors (York Playhouse), Wolf at the Door, Invisible Friends (Scarborough, Stephen Joseph Theatre).

Leading roles at the National Theatre include Angels in America (1992), Rutherford and Son (1995), Fair Ladies at a Game of Poem Cards (1999), The Prince's Play (2000), Sleep With Me (2002).

Other leading roles in television include The Black and Blue Lamp (BBC), No Further Cause For Concern (BBC), Ellington (ITV), Peak Practice (ITV), Kavanagh QC (ITV), Midsommer Murders (ITV), Trial and Retribution V (ITV) and Murphy's Law (ITV). He has also featured in various episodes of French & Saunders and in Absolutely Fabulous. He appeared in the episode The Raven in the Foregate from the third series of Cadfael in 1997 as a medieval murder suspect and spy.

His work in London theatre is also extensive. Leading roles include Enemies (Almeida 2006), A Prayer for My Daughter (Young Vic, 2007).