Chapman was commissioned into the 3rd Durham Royal Garrison Artillery, although his unit later transferred to the Royal Field Artillery (Territorial Force). Chapman was the son of Henry Chapman and Dora Gibson. lieutenant was usually a safe seat for the Labour, but fell to the Conservatives as one of their many gains that year, when Labour split over budgetary policy and Ramsay MacDonald formed a National Government.
Chapman was defeated by the Labour candidate at the 1935 general election, and did not stand for Parliament again.
He was High Sheriff of Durham in 1940. In 1958 he was created a baronet, of Cleadon in the County of Durham.
Chapman married Hélène Paris, daughter of James George MacGowan, in 1909.