On stage, wearing his black beret, goatee, and wire-rimmed glasses, Dizzy Gillespie was the much-imitated archetype of the jazz hipster. When he raised his trademark bent horn and began to play, cheeks puffed out like a giant chipmunk, he created a sound that defined American jazz, and many of his compositions become lasting jazz standards. Gillespie came of age during a golden time in jazz. In the 1930s and 1940s, brilliant musicians like Gillespie, Charlie Parker, Thelonious Monk, Miles Davis, and Max Roach were playing together in wildly creative jam sessions that would change the face of American music. Though Gillespie's technical expertise and soaring harmonies on the trumpet made him an integral part of this new movement, perhaps his greatest contribution was his ability to thrive as an African-American musician and public figure in the inhospitable climate of the pre-civil-rights United States. During...