Chapman served with the Royal Australian Air Reserve from 1953 to 1955. From 1956 to 1957, he worked for Philips Electronics Industries Proprietary Limited in Sydney, Australia. He then joined the Australian National Antarctic Research Expedition (IGY) serving for two years as an auroral/radio physicist..
From 1960 to 1961, he was an electro-optics staff engineer in flight simulators for Canadian Aviation Electronics Limited in Dorval, Quebec. His next assignment was a staff physicist at the Massachusetts Institute of Technology, where he worked in electro-optics, inertial systems, and gravitational theory until the summer of 1967. He has logged 1000 hours flying time in jet aircraft.
Dr. Chapman was selected as a scientist-astronaut by NASA in August 1967. After initial academic training and a 53-week course in flight training at Randolph Air Force Base, Texas, he was involved in preparations for lunar missions, serving in particular as mission scientist for the Apollo 14 mission. Because of the lack of spaceflight opportunities for scientist-astronauts in the 1967 intake, Dr. Chapman left NASA in July 1972.