Based on IBDB, The Ed Sullivan Theatre was originally call the Hammerstein's Theatre when it was built in 1927. It was also called Manhattan Theatre in 1931 and Billy Rose's Music Hall in 1933. Then the name was changed back to Manhattan Theatre in 1936. CBS then came along, also in 1936, and it was renamed CBS Radio Playhouse No. 1 followed by CBS Studio No. 50 in 1950. In 1967 it was finally named The Ed Sullivan Theatre. Also based on IBDB, the last official Broadway Play to be performed there was something called Help Yourself Written by John J. Coman in 1936. I assume that if there was something there before Letterman it was not considered a Broadway production.
"Smart! And into all those exotic mystiques -- The Kama Sutra and Chinese techniques. I hear she knows more than seventy-five. Call me tomorrow if you're still alive!"