Ordained as a priest by Bishop Joseph Chartrand on September 9, 1916, he then taught at his alma mater of Notre Dame, of which he was also spiritual director. He served as Instructor of Religion, Dean of the College of Commerce, Vice President (1933–1934), and President (1934-1939) of Notre Dame. He was also one of the directors of Catholic army and navy chaplains during World War II.
On December 11, 1939, O'Hara was appointed Apostolic Vicar for the US Military Forces and Titular Bishop of Milasa. He received his episcopal consecration on January 15, 1940 from Archbishop Francis Spellman, with Bishops John Noll and Joseph Ritter serving as co-consecrators, in Sacred Heart Church. He was named the eighth Bishop of Buffalo on March 10, 1945, and was promoted to the fifth Archbishop of Philadelphia on November 23, 1951.
As Philadelphia's archbishop, O'Hara condemned the Supreme Court's ruling against banning the films La Ronde and M. Moreover, not overly favorable of radio and television, he suggested that his flock sacrifice such entertainment for Lent.
He was created Cardinal Priest of Ss. Andrea e Gregorio al Monte Celio by Pope John XXIII in the consistory of December 15, 1958. O'Hara died following surgery in Philadelphia, at age 72. He is buried in Sacred Heart Church at Notre Dame, Indiana.
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