Abandoned as a child and having grown up in an orphanage, Kirby struggled to the top of his profession as a jazz musician in 1920s New York, joining one of the city's leading big bands, the Fletcher Henderson Orchestra, on tuba and double bass in 1930.
He was a strong tuba player but soon emerged as an even more distinctive string bassist, injecting life and momentum into Henderson's rhythm section on pieces like the 1930 disc Chinatown My Chinatown. In the early to mid 1930s, he played alternately for Henderson and Chick Webb, recorded widely as a freelance, and formed his own group in 1937 at the Onyx Club on 52nd Street.
Soon the personnel stabilised into a sextet, with Charlie Shavers, trumpet; Buster Bailey and Russell Procope, reeds; Billy Kyle, piano; and O'Neill Spencer, drums. Using neatly crafted arrangements, that required fantastic control and precision from his players, his group was soon billed as 'The Biggest Little Band in the Land'.
Not only did his intricate versions of pieces like Close Shave and Undecided define small group chamber jazz in the swing era, but they became the template for the musicians who would experiment with developing bebop, using just such knotty unison 'head' arrangements before opening their pieces up for solo playing. Kirby's own fortunes barely lasted into the bebop era.
When the original personnel of his band broke up in 1942, he kept going for another four years with numerous changes (including Dizzy Gillespie on trumpet), but after separating from his wife, the singer Maxine Sullivan, Kirby went into a decline. He made a few efforts to rekindle his band, but eventually fell victim to drink and diabetes at the age of 43.