Chester James Parker was born on 29 July 1916 in Charters Towers, Queensland, to James Athol Parker (1875-1954) and Margaret Ann (née Brennan) (1894-1974). He attended the Townsville Grammar School, then enrolled as an undergraduate in the Faculty of Arts of the University of Queensland in 1935. In 1938, he was selected as the Queensland Rhodes Scholar. He intended to pursue a career in law. Parker was engaged to Winifred Hanger. At the outbreak of World War Two, Parker joined the Royal Naval Volunteer Reserve and he and Winifred exchanged letters and telegrams throughout his service. He was serving as a Lieutenant on HMS Thorn, a submarine of the Royal Navy, on 6 August 1942 when she encountered Italian torpedo boat Pegaso. HMS Thorn failed to return from patrol and was presumed sunk 'with all hands'. Parker is commemorated on the Portsmouth Naval Memorial.