If Father Bill Sheehan were your parish priest, the pews would be packed for every Mass he said. As it is, he’s in huge demand all over the country to lead retreats where everyone sits for hours a day, eyes closed, in a silent meditation known as Centering Prayer.

And his retreats are packed.

“He’s the best of the best. There’s a light in him and a sweetness and gentleness that you’re very drawn to,” says Nancy Nichols Kearns, a long-time Centering Prayer practitioner and volunteer with Boston’s chapter of Contemplative Outreach, Centering Prayer’s umbrella organization.

Bill Sheehan himself is more modest.

“I just think people are searching for something deeper, and sometimes they don’t even know how to articulate that,” he said at home in Lowell, Massachusetts, where he is a priest with the Oblates of Mary Immaculate. “I’ll be flying to a retreat wearing my Oblate cross, reading or preparing. Inevitably the person next to me will ask, ‘Where are you going? What are you doing?’ ‘I’m going to a retreat center in Amarillo (Texas),’ I’ll say. ‘Oh?’ I’ll tell them I’m a Catholic priest and I’m giving a retreat there and then, boom, Catholic, not Catholic, Christian or not, they want to know all about it.”

There’s a fascination there, a curiosity, maybe even a holy yearning like the one he finds among those making his retreats for a day, a weekend, a week or more. At the start of each retreat, he asks participants why they’re there and what they’re looking for. “They’re looking for silence,” Sheehan says. “And they’re looking for a deeper relationship with God. There’s just that attraction.”

As someone who’s felt that attraction, too, I’m amazed there aren’t Centering Prayer groups in every Catholic parish around, particularly now, when we hear so much about the need to slow down, unplug, live “mindfully” in the moment, and meditate. Centering Prayer offers a path to all that. More important to Catholics, as its co-founder the Trappist monk Thomas Keating has said, it offers the chance to experience the presence of God — even if you’re no paragon of perfection yourself.

Perhaps Centering Prayer has struggled in parish acceptance because it’s relatively new and unknown to many priests. Or perhaps it’s because the tradition-bound Catholic Church is not the first place would-be meditators would look for guidance.

Here’s the story, legendary in Centering Prayer circles, about Keating and his not exactly hip and trendy monks being bypassed for the always hip and trendy Buddhists. This was back in the 1970s, though the Catholic-to-Buddhist hipness gap surely remains today. Keating and his fellow Trappists William Meninger and Basil Pennington were living in a community at St. Joseph’s Abbey in Spencer, Massachusetts. They noticed how often young people in sandals and faded jeans were knocking at their door, but not seeking them. No, they were usually lost and looking for directions to the Buddhist meditation center down the road. This — plus a Vatican II decree to clergy to revive the contemplative dimension of the Gospel — inspired these monks to explore and eventually update ancient Catholic meditative practices with roots in the Desert Fathers, early Benedictine monasticism, and “The Cloud of Unknowing,” a late 14th-century text by an anonymous monk.

Thus, in 1975, Centering Prayer was born. Sheehan met Keating and the prayer just a few years later. Keating was wondering then if laypeople, not just nuns and priests, could move into this tradition and invited Sheehan to join a small group at a 14-day retreat at the Lama Center in the mountains of New Mexico.

“Back then, there was no electricity, no indoor water, just outhouses and an outdoor shower. Inside at night it was all candles,” Sheehan remembers. “For the first time, my life was reduced to utter simplicity, just the basics, and it was fine. Then to be plunged into the silence and several hours of prayer throughout the day, with Thomas (Keating), well, it was a very powerful experience.”

That was more than 30 years ago. In 1986, Contemplative Outreach Ltd was formed to share the teaching of Centering Prayer. It is now practiced by tens of thousands in nearly 50 countries and, as I said, in a smattering of American Catholic parishes.

What exactly is it? Most simply, it’s a prayer method where a person chooses a sacred word — Amen, Jesus, Abba, whatever — and sits with eyes closed for 20 or 25 minutes, twice a day, returning gently to the word when thoughts arise. In the beginning, that’s all the time. The idea is to gradually learn to rest in God, to be open to God’s presence, to develop both a relationship with God and a discipline to foster that relationship.

Keating, now 92, has written many, many books on the practice. He tells you that your way of seeing reality, sooner or later, will change. It’s like the difference between watching a black-and-white TV and a color TV. Regular practitioners will tell you they experience less fear and judgment and more calm, patience, generosity. They live life more abundantly, as John’s Gospel puts it. Bill Sheehan has told me and others during retreats I’ve made with him that it’s not about my own worthiness, how good I am or am not (what a relief). Instead it’s about showing up to the prayer, day after day, “to trust, receive, let go, surrender.”

“It’s a love story,” he says, “initiating from Him.”

Sitting across from Sheehan in his Lowell office, I can see in his face and hear in his voice what decades of “showing up” has done for him and his own love story. I want what he’s got.

Bill Sheehan is not far from 80 years old. He doesn’t look it. His blood pressure is terrific, he tells me, another “fruit” of all that prayer. “How long can I do this?” he says, referring to flying all around the country giving retreats. “I don’t have a clue. But I say that as long as I’ve got something on the calendar, I’m going to be okay. I’ve put dates down for 2016, and I’ve got some in 2017.

“Let me tell you: At my age, someone’s always asking, ‘Are you retired?’ And I say, ‘Not quite.’ I tell them I’m spending most of my time hanging out with people who are searching for God.”