In 1843, Fahy was appointed by the Archbishop of Dublin Daniel Murray to the Irish chaplaincy of Buenos Aires in place of father Patrick O'Gorman.
Fahy organized his flock in chaplaincies in Buenos Aires province, and appointed twelve Irish priests to these areas.
Fahy sponsored the training of a number of priests from Ireland, in All Hallows College, Dublin, for the Argeintine mission, these included Fr.
Anthony Fahy died of a heart attack on 20 February 1871; according to other sources he was victim of a cholera outbreak that killed thousands of people in Buenos Aires in 1871.
In the association of ex-alumni of the "Instituto Fahy" is located the practice centre of "Celtic Argentina", an Argentinian stepdancing group.