His father, Edward Tinsley "Ned" Chase (1919–2005), was a Princeton-educated Manhattan book editor and magazine writer. Chase's paternal grandfather was artist and illustrator Edward Leigh Chase, and his great-uncle was painter and teacher Frank Swift Chase. His mother, Cathalene Parker (née Browning; 1923–2005), was a concert pianist and librettist, whose father, Rear Admiral Miles Browning, served as Admiral Raymond A. Spruance's Chief of Staff on the aircraft carrier USS Enterprise at the Battle of Midway in World War II. Cathalene was adopted as a child by her stepfather, Cornelius Vanderbilt Crane, heir to The Crane Company, and took the name Catherine Crane. Her mother, also named Cathalene, was an opera singer who performed several times at Carnegie Hall.

Chase was named for his adoptive grandfather, Cornelius, while the nickname "Chevy" was bestowed by his grandmother from the medieval English ballad "The Ballad of Chevy Chase". As a descendant of the Scottish Clan Douglas, she thought the name appropriate.