Vance entered the military during World War II, serving in the United States Navy as a gunnery officer on the destroyer USS "Hale" (DD-642) until 1946. He saw sea action in the Battle of Tarawa, the Battle of Saipan, the Battle of Guam (1944), the Bougainville Campaign, and the Philippines Campaign (1944–1945). After the war, he worked for the Mead Corporation for a year before joining the law firm Simpson Thacher &amp; Bartlett in New York City.