Godfrey was born in Manhattan in 1903. His mother, Kathryn Morton Godfrey, was from a well-to-do Oswego, New York, family which disapproved of her marriage to an older Englishman, Arthur's father, Arthur Hanbury Godfrey. The senior Godfrey was a sportswriter and considered an expert on surrey and hackney horses, but the advent of the automobile devastated the family's finances. By 1915, when Arthur was 12, the family had moved to Hasbrouck Heights, New Jersey. Godfrey dropped out after a year at Hasbrouck Heights High School. Arthur, the eldest of five children, had tried to help his family survive by working before and after school, but at age 14 left home to ease the financial burden on the family. By 15 he was a civilian typist at Camp Merritt, New Jersey, and enlisted in the Navy by lying about his age two years later.