Dublin native Paddy Moloney taught himself how to play the tin whistle when he was six and learned the basics of music at school each day. Shortly after, he picked up the Uilleann pipes, and was taught by master piper Leo Rowsome.

Moloney was not influenced by other players. Instead, he developed his own style. He listened to old 78-rpm recordings and visited older musicians who took him under their wing. When he was a teenager, he entered musical competitions in Dublin's Feis Atha Cliath and won several all-Ireland medals. Before long, he was making friends with several other Irish musicians committed to keeping traditional folk music alive.

Moloney performed with a number of groups in Dublin, including The Happy Wanderer and The Loch Gamha Ceili Band, and then joined arranger/composer Seán Ó Riada's folksy chamber orchestra, Ceoltóirí Cualann. The group proved to be a sparkplug for interest in Irish traditional music and paved the way for the birth of The Chieftains.

In 1962, when the opportunity to record for Claddagh Records came along, Moloney formed his own band with fiddler Martin Fay, flute player Michael Tubridy, tin whistle player Seán Potts and bodhrán player Davy Fallon, thereby launching The Chieftains.