The New York Times confirmed the Wednesday death of the classically trained violinist, but did not report the cause.
Established in 1962, the Chieftains became famous worldwide after providing the music for Stanley Kubrick's 1975 film, "Barry Lyndon."
Appointed official musical ambassadors for the Republic of Ireland in 1989, the Grammy Award-winning band recorded 40 albums and played with the Rolling Stones, the Boston Pops, Willie Nelson and Luciano Pavarotti.
The Times said Fay retired from the Irish folk group in 2002.
He is survived by his son; his wife, Gertie; his daughter, Dearbhla Fay; a sister; and a grandson, the newspaper said.