The Chieftains recorded their first album in 1962. Like Cherish the Ladies, it was supposed to be a one-time deal. They reunited 5 years later and made a second album. Three more albums followed with different members coming and going. As far as I can tell, they were an in-studio band only, maybe touring part-time. In 1975 they started going at it full time with the classic lineup.
Got this from their website: