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Slattery was ordained to the priesthood by John Cardinal Cody on April 26, 1966, and then served as associate pastor of St. Jude the Apostle Parish in South Holland until 1971. During this time, he also earned a Master's degree from Loyola University. He was Vice-President (1971–76) and President (1976–94) of the Catholic Church Extension Society, a Chicago-based funding agency for the American home missions. While working at Extension, he was named associate pastor at the inner-city Hispanic parish of St. Rose of Lima on the south side of Chicago in 1973. He later served as pastor of St. Rose of Lima from 1976 to 1989.