Chapman graduated from The London Academy of Music and Dramatic Art (LAMDA) in 1992 and was trained at the Jim Henson Company's puppeteering workshop in 1994. His tutors were Kevin Clash, Nigel Plaskitt, and Rob Tygner. Afterwards, Chapman performed various puppet characters for British TV; such as BBC presenters Otis the Aardvark and Vinnie the Ferret. He has also performed Tiny of Tiny and Mr Duk, Scratch on Nuzzle and Scratch, and Windy on Space Pirates.
Chapman's acting credits includes the BAFTA Award winning shows The Slammer and Dick and Dom in Da Bungalow (in the latter, he played over 200 characters). He also provided Dalek voices in the 1999 special Doctor Who and the Curse of Fatal Death.