He studied medicine at the University of Cambridge, gaining a Bachelor of Medicine, Bachelor of Surgery (Bachelor of Medicine BChir), Master of Arts (Master of Arts) and Doctor of Medicine (Doctor of Medicine).
He has been the director of the Division of Medicine and Cancer at Westmead Hospital in Sydney since 2007. From 1984 to 1987, he was a lecturer and research fellow at the University of Oxford. Chapman migrated to Australia in 1987, and commenced lecturing at the University of Sydney and practicing medicine at the newly opened Westmead Hospital.
He served as President of The Transplantation Society between 2008 and 2010.
Chapman is a Board member of the Western Sydney Local Health District, Westmead Medical Research Foundation, and is Chairman, Australian Bone Marrow Donor Registry, since 1991 and Manager of the Australian National Kidney Matching Service, since 1988.