Chestnut is a surname. Notable people with the surname include:
- Ashlei Sharpe Chestnut, American actress
- Ben Chestnut, American billionaire tech executive
- Charles S. Chestnut IV (born 1962), American politician
- Cynthia M. Chestnut (born 1949), American politician
- Cyrus Chestnut (born 1963), American jazz pianist, composer and producer
- Harold Chestnut (1917–2001), American electrical engineer, control engineer and manager at General Electric and author
- J. L. Chestnut Jr. (1930–2008), African-American attorney and civil rights activist
- Jacob Chestnut (1940–1998), one of two Capitol police officers killed in the U.S. Capitol shooting incident
- Jennings Chestnut, American luthier
- Joey Chestnut (born 1983), American competitive eater
- Julius Chestnut (born 2000), American football player
- Morris Chestnut (born 1969), American film and television actor
- Randy Chestnut (born 1971), American comedian
- Johnson Chesnut Whittaker (1858–1931), American, one of the first black men to win an appointment to the United States Military Academy at West Point