Provenza was born and grew up in the Pelham Parkway section of the Bronx, New York City, and graduated in 1975 from the Bronx High School of Science. In high school, he started performing stand-up comedy, making his stage debut at age 17 at the original The Improv in Manhattan. He continued performing while attending the University of Pennsylvania, taking a year's leave of absence to study in London at the Royal Academy of Dramatic Arts. While at RADA, he joined a classical repertory theater group, becoming one of few Americans to perform the role of Romeo on the London stage. He graduated in 1979 from the University of Pennsylvania, the year it awarded its first Theatre Arts degree. At Penn, he wrote for the Pennsylvania Punch Bowl and was a cast member of the Mask and Wig Club, where he has returned numerous times to perform in the annual Intercollegiate Comedy Festival.