The general chapter is intended to end a three-year period of papal receivership after Pope Benedict XVI imposed a delegate to take control of the order in 2010.
That decision followed revelations of sexual abuse and misconduct by the founder, the late Mexican Fr. Marcial Maciel Degollado, as well as defections by several high-profile Legionaries and speculation that the order might be suppressed.
Legionaries taking part in the chapter meeting who spoke to NCR in January insist there's widespread agreement on several fronts, including the need for less control from Rome and more autonomy for local Legionary operations, a greater tolerance for interval diversity, and a new commitment to transparency.
They also say they've made progress toward defining a post-Maciel charism, or mission, for the Legion, focusing on a commitment to evangelization, meaning a missionary drive, and the Legion's partnership with Regnum Christi, its lay movement.
Yet they say it's also clear there's a range of opinion inside the order over just how far reform ought to go.
Some Legionaries, these sources say, believe that much about their older ways of doing business retain value, citing what they see as the "spiritual fruits" the Legion has produced over the years.
At the opposite end of the spectrum, there are other Legionaries anxious to see reform reach more deeply and move more quickly. Some priests in that camp have already left, and privately, Legionaries concede that others may yet do so.
One focal point for this tension, Legionaries say, is the Maciel legacy.
Fr. John Connor, a Legionary priest based in New York, told NCR that the current general chapter meeting is committed to upholding a 3-year-old policy that Maciel will no longer be referred to as "Our Father," that pictures of him will be removed from Legionary facilities, and that his writings won't be used in formation programs.
"We all understand that he can't be a model of Christian life, religious life or Legionary life," he said.
Yet Fr. John Bartunek, a Cleveland native now based in Rome, said there's disagreement over other matters, such as the extent to which Maciel's spiritual writings retain value.
"A lot of the fathers fed their hunger for spiritual reading with the writings of the founder," Bartunek said. "Today, a lot of these guys are doing great work and are spiritually mature priests, and they ask, 'How can we say it's all trash?' "
"We're not going to resolve [that tension] quickly," he predicted. "We're going to have to live with it for a while."
Privately, Legionaries say those tensions form part of the politics of choosing a new leader. Sources told NCR that participants in the general chapter may seek a compromise candidate, meaning a figure acceptable to Legionaries along the spectrum from wanting immediate change to going it slow.
The order posted a notice on its website on Jan. 20, stating that the general chapter had moved into the elections phase, but there's been no indication of the results. Before making any announcement, the Legion has to wait for Pope Francis to sign off.
In the meantime, the general chapter is continuing to work on a new set of constitutions for the order, with a Tuesday web post by the Legion indicating much of the work on the first two sections has been completed.
An official told NCR Tuesday that once the constitutions receive Vatican approval, they'll be released to the public.
The general chapter meeting is being presided over by Italian Cardinal Velasio de Paolis, the official appointed by Benedict and confirmed by Francis to oversee the reform effort.
Italian Jesuit Fr. Gianfranco Ghirlanda, the former dean of the canon law faculty at Rome's Jesuit-run Gregorian University and later the university's rector, is also on hand, providing advice on matters of church law.
Though the general chapter has no firm end date, it's expected to last into February.
Sixty-one priests from 10 countries are taking part, including seven Americans.