He made his acting debut in 1964 in the series Curtain of Fear, and is best known for his recurring roles as Captain George Brent in Colditz (1972–74) and Stephen in As Time Goes By.
Since graduating from RADA (Royal Academy of Dramatic Art) in the early 1960s, he has had an extensive career on stage and on screen.
He has a number of high-profile television series to his name, including The Adventures of Sherlock Holmes, A Bit of a Do, Fairly Secret Army, Pie in the Sky and Midsomer Murders.
Chapman's other TV credits include Waiting for God ("The Helicopter" episode as Councillor Ferguson), and in the BBC's 1971 adaptation of Jane Austen's Persuasion, as Captain Benwick.
In December 1971 he created the role of Nogbad the Bad in a Birmingham stage adaptation of the animated TV series Noggin the Nog.