Allan Chapman (18 March 1897 – 7 January 1966) was a Scottish Unionist Party politician. Chapman was the son of H. Williams Chapman and attended Queens' College, Cambridge. He was elected at the 1935 general election as Member of Parliament (MP) for the Rutherglen constituency in Lanarkshire. He held the seat during the war years, but at the 1945 general election he was defeated by the Labour Party candidate Gilbert McAllister. He was married to Beatrice Cox. He died at Dundee Royal Infirmary, age 68.