Henry was the son of George W. Chapman, lieutenant in the United States Army, and Emily, granddaughter of Abraham Markoe, first captain of the Philadelphia City Troop.

He entered the Pennsylvania Hospital, first as an assistant in the apothecary shop, and later as a resident physician, but in 1869 went to Europe for three years' study with Sir Richard Owen, London; Alphonse Milne-Edwards, Paris; Emil du Bois-Reymond, Berlin; and Josef Hyrtl, Vienna.

Meigs died in the autumn of 1879, soon after starting his lectures for the term, and the course was continued by Chapman who, in 1880, was appointed to the vacant chair of institutes of medicine and medical jurisprudence.

Chapman wrote much on the anatomy of apes and was fortunate in securing a gorilla (1878) and a chimpanzee (1899) for dissection; practically all the valuable material coming out of the Philadelphia Zoological Garden passed through his hands.

He records in a report that his experience as prosector showed "that the principal causes of deaths during the first six months of the existence of the Garden were improper food, badly regulated temperature and ill constructed cages."