O'Brien was born in Indianapolis, Indiana, and attended St. Meinrad Seminary. Feeling a call to the priesthood from an early age, he was ordained for the Diocese of Tucson, Arizona, on May 7, 1961. He then served as an associate pastor at Immaculate Conception Church in Douglas. In 1964, O'Brien was transferred to territory that would later become the Diocese of Phoenix, as an associate pastor at and later at St. Gregory Church. He was named pastor of St. Catherine Church in Phoenix in 1979, and also served as vicar general for the Diocese.
In 1990, O'Brien oversaw the development and implementation of a diocesan policy to investigate sexual abuse cases involving priests. The policy was revised in 1995 and 1998, with many of its policies being adopted in the 2002 Dallas Charter. In 2002, Maricopa County prosecutors initiated a grand jury investigation into charges of sexual abuse by Catholic priests in the diocese of Phoenix. Bishop O'Brien was a target of that investigation for allegedly covering-up allegations against other priests. The prosecution ended when the bishop admitted he had sheltered abusive priests. O'Brien agreed to cede his authority over diocesan sexual abuse policy in exchange for immunity from indictment for obstruction of justice. On August 4, 2017, it was announced that a civil lawsuit was filed against O'Brien over allegations that he sexually molested a boy on several occasions at parishes in Phoenix and Goodyear from 1977 to 1982.
On June 14, 2003, less than two weeks after signing a sexual abuse agreement with prosecutors, O'Brien was driving home from a confirmation ceremony when his vehicle struck a 43-year-old pedestrian named Jim Reed. Reed subsequently died from injuries. A driver behind O'Brien reported O'Brien's license plate number to the police. Police discovered a dent in a fender and a crack in the windshield of the bishop's Buick Park Avenue. O'Brien said he did not report the accident because he thought he had hit a dog, cat, or rock. He was arrested for leaving the scene of an accident and released on $45,000 bond. He resigned as Bishop on June 18, 2003. On February 17, 2004, after a three-and-a-half-week-long trial, O'Brien was found guilty of leaving the scene of a fatal accident. On March 26, 2004, he was sentenced to four years' probation and 1,000 hours of community service, and required to surrender his driver's license for five years. He was the first American Catholic bishop to be convicted of a felony. O'Brien later asked for travel time to be deducted from his 1,000 hours and for flexibility in the number of hours he must serve each month.
Death
O'Brien died on August 26, 2018 following complications from Parkinson's disease.
In November 2011, the Catholic Community Foundation of Phoenix announced that it was giving O'Brien its faith honoree award. When news of the intended award became public, a controversy emerged over the decision. A few days later, O'Brien declined the award, and the foundation, stating that it did not anticipate the adverse public reaction, wrote an apology to the community.