The left-handed virtuoso banjo player was born in New Orleans, Louisiana, the son of well regarded string bass player Henry Kimball. He was playing music professionally by the mid-1920s with such groups as the bands of Fate Marable and Papa Celestin. He married a fellow member of Celestin's Tuxedo Jazz Band, pianist Jeannette Kimball (née Salvant).
In the 1930s during the Great Depression Kimball switched to string bass to play in swing bands such as Sidney Desvigne's, but music did not provide enough money; and he got a day job as a mailman. He continued playing music in the evening, leading his band called "Narvin Kimball's Gentlemen of Jazz".
With the revival of interest in traditional jazz, about 1960 was able to return to regularly play banjo professionally again. He played regularly at such French Quarter venues as Preservation Hall and Dixieland Hall, at the latter often leading a band under his own name. However he kept his day job as a postman until his retirement in 1973; until then he only took brief tours outside the city while on vacation from his postal job. After this date, he toured the United States and Europe extensively with the Preservation Hall Jazz Band. His singing "Georgia on My Mind" was a reliable show stopper. He was the oldest member of the band at his retirement in 1999 at age 90.
When Hurricane Katrina was threatening New Orleans, in 2005, Preservation Hall leader Ben Jaffe made a point to make sure Kimball and his wife were evacuated to Baton Rouge. He died in exile with relatives in South Carolina.
- Obituary by Peter Vacher, The Guardian, 25 March 2006 
- Obituary by Dick Parker, Coda
- New Orleans Jazz: A Family Album by Al Rose and Edmond Souchon, Third Edition, Louisiana State University Press, 1984
- Preservation Hall by William Carter, W.W. Norton & Company, 1991
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