York was born in Fort Wayne, Indiana, to Betty, a seamstress, and Bernard York, a salesman. He grew up in Chicago, where a Catholic nun first recognized his vocal promise. He began his career at the age of 15 as the star of the CBS radio program "That Brewster Boy". He also appeared in hundreds of other radio shows and instructional films before heading to New York City, where he acted on Broadway in "Tea and Sympathy" and "Bus Stop". He performed with stars including Paul Muni and Joanne Woodward in live television broadcasts and with Janet Leigh, Jack Lemmon, and Glenn Ford in movies, including "My Sister Eileen" and "Cowboy".