Stone was born in Los Angeles to Jewish parents. His mother, Hilda (née Hess), was a film writer, and his father, John Stone (born Saul Strumwasser), was the writer and producer of many silent films, including Tom Mix, Buck Jones, Shirley Temple and Charlie Chan movies. Hilda was a Bavarian Jew from Bamberg, but was born in Mexico (her father dodged the draft back in the 1870s) and lived there for five years with her family until all foreign nationals were kicked out during the Mexican Revolution of 1910. Stone has a brother David, who was a World War II veteran, serving with the U.S. Navy.