Pope Benedict XVI will convene a meeting this week in the Vatican to discuss whether the vows of celibacy and the ban on marriage for priests who want to marry, or have married in the past, should be overturned.
In the eyes of current church doctrine, priests who get married are committing an act of heresy.
The man at the center of the controversy is Emmanuel Milingo, a flamboyant Zambian exorcist who in 2001 married his wife in the Unification Church at a Mass wedding presided over by the Rev. Sun Myung Moon.
Flouting the rule of celibacy cost Milingo, an archbishop, whose wife was chosen for him by Moon, his position in the church.
Pope Benedict XVI excommunicated Milingo in September, after he ordained four married bishops in Washington.
Among them was Peter Brennan, who is part of the organization Married Priests Now.
"In December we will be meeting. We're hoping to attract 1,000 married priests," Brennan said.
A married Italian priest will hold a prayer vigil in St. Peter's Square tonight, hoping to influence Pope Benedict, who will hold what amounts to a cabinet-level meeting to reflect on the crisis Thursday.
"I think it would be an insult to the priests who have remained faithful to readmit these individuals who have left the priesthood in order to marry," said Archbishop John Foley, a Vatican spokesman.
As foreign as the concept may seem today, the first pope, St. Peter, was married.
Catholic priests were allowed to be married until the 12th century.
But Pope Benedict, a stalwart conservative, is unlikely to relax a rule that has been in place nearly 1,000 years.