Dr. Chapman was born in Jefferson County, New Jersey, the son of a physician, and educated locally. He attended Syracuse University (1898) and the University of Michigan, where he completed his medical training in 1905. He later received training at the New York State Psychiatric Institute.
He began general practice in Watertown, New York, and in 1906 took an appointment at the Utica State Hospital, transferring to the Binghamton State Hospital in 1907, where he remained until 1916. He became interested in psychoanalysis as well as hospital administration and, in 1916, moved to St. Elizabeths Hospital in Washington, DC, as the first assistant physician to Dr. William A. White.
In 1920, Dr. Chapman became superintendent of the Sheppard and Enoch Pratt Hospital in Baltimore, MD, where he remained until 1948. During WWI, he was a major in the Army Medical Corps, serving as a division psychiatrist, and later in the Army of Occupation. He served as a Professor of Psychiatry at the University of Maryland after 1920. He was an active member of professional organizations including the American Medical Association, the American Psychopathological Association (President 1928), the American Psychoanalytic Association, and the American College of Physicians. He published a number of papers on psychiatric subjects.
Dr. Chapman served as President of the American Psychiatric Association (1937–38).