Baron was born on June 26, 1955, in Richmond Virginia. When he was nine, he taught himself how to play the drums. As a teenager, he played in rock bands and dixieland jazz groups. After high school, he spent a year at the Berklee College of Music. He moved to Los Angeles in the early 1970s and embarked on a professional career, playing with Carmen McRae and Al Jarreau. He worked as a freelance drummer and session musician with Chet Baker, Stan Getz, Dizzy Gillespie, and Hampton Hawes.In 1982 he moved to New York City and joined guitarist Bill Frisell, with whom he would play often throughout his career. He also played in groups with Red Rodney, Fred Hersch, Enrico Pieranunzi, and Marc Johnson. Starting in the late 1980s, he became a bigger part of the avant-garde jazz scene when he played regularly at the Knitting Factory, recorded with singer Laurie Anderson, and began a long association with John Zorn. For several years he participated in Zorn’s projects Naked City and Masada.