Kercheval trained under Sanford Meisner at The Neighborhood Playhouse in New York City. Kercheval made his Broadway debut in the 1962 play Something About a Soldier. He appeared off-Broadway in the 1963 Kurt Weill revue From Berlin to Broadway, and can be heard on the cast recording. Additional theatre credits include The Apple Tree, Cabaret (replacing Bert Convy as Cliff), and Here's Where I Belong. In 1966, he appeared as the title character in the original Broadway production of Fiddler on the Roof, co-starring with Herschel Bernardi, Maria Karnilova, Julia Migenes, Leonard Frey, and Pia Zadora.