Owsley was born in Chicago, Illinois, in 1883. His father was Heaton Owsley (1856–1930), an Illinois native and manufacturer. His mother, Harriet (Byrne) Owsley was a Mississippi native who died in the same year that Owsley was born. He was the nephew of Carter Harrison, Jr., the mayor of Chicago from 1897 to 1905. Owsley attended preparatory school at the Phillips Academy in Andover, New Hampshire, graduating in 1902.