In 1960 Ó Riada was looking for musicians to perform music for the play "The Song of the Anvil" by Bryan MacMahon. Paddy Moloney, at the age of 20, was called to participate in the project, along with his friend Sean Potts on tin whistle, Sonny Brogan on accordion and John Kelly on flute. They rehearsed weekly in Ó Riada's house in Galloping Green, on the outskirts of Dublin.
Following its success, Ó Riada had the idea of forming Ceoltóirí Chualann, a band to play traditional Irish songs with accompaniment and traditional dance tunes and slow airs, arranged with instruments: harpsichord, bodhran, piano, fiddle, accordions, flute, pipes and whistles. The idea of actually arranging folk music, or dance music, had been done on at least one or two 78rpm recordings in the past, but they were folk tunes done in a classical way, highly orchestrated. Another aim was to revitalize the work of blind harpist and composer Turlough O'Carolan.
The band was launched during the Dublin Theatre Festival in September 1960, at the Shelbourne Hotel, at an event called Reacaireacht an Riadaigh (Ó Riada's Recital). Included in the program were tradtional singers, writer Seán Ó Riordáin and poet Seán Ó Tuama. In March of the following year Ó Riada recorded the first of a series of radio programmes for which he retained the name Reacaireacht an Riadaigh, and included music played by Ceoltóirí Chualann. Soon after the band's formation, Peadar Mercier and Seán Keane joined.
Ceoltóirí Chualann continued to play until 1969. During that year they recorded two albums, Ó Riada and Ó Riada Sa Gaiety. The latter of those two albums was not released until after 1971, when Seán Ó Riada died.