Hurt, whose father worked for the State Department, was born in Washington, D.C., and traveled widely as a child while attending boarding school in Massachusetts. His parents divorced when he was young. When Hurt was 10, his mother married Henry Luce III, son of the Time magazine founder. Hurt studied acting at Julliard and first emerged on the New York stage with the Circle Repertory Company. After The Big Chill, he returned to the stage to star on Broadway in David Rabe's Hurlyburly, for which he was nominated for a Tony.