It’s just before the end of Act 1 of “The Book of Mormon,” and Christopher John O’Neill is singing about Jesus.

O’Neill knows the words. He knows he knows the words. The song is “Man Up.” His character, the bumbling self-proclaimed sidekick Elder Cunningham, is getting his Mormon game face on. O’Neill is sweating. He’s sweating a lot, actually; has he ever sweated so much in his entire life? It’s just that it’s really hot onstage at the Kennedy Center. The bright lights. The heavy costumes. There’s a lot of dancing, okay? You’d sweat too, probably.

“Man Up” is what O’Neill sang at his first audition. He was in some studio in Midtown, when the whole idea of being in this show — the first national tour of “The Book of Mormon,” with nine Tony Awards and a gazillion bucks in ticket sales to its name — was a joke, a fantasy. But when somebody asks if you want to try out for a lead part in the most popular show in America, you don’t say, “Actually, I’m a sketch comedian with absolutely no professional musical theater experience.” You ask your girlfriend to take a photo of you on the roof of your place in Queens, you get the image copied, and you and your homemade headshot hightail it to Manhattan.

O’Neill, 31, wasn’t new to performing in public; he and his comedy partner, Paul Valenti, had been writing and starring in their comedy act, “The Chris and Paul Show,” since 2000. They’d toured the United States and made it to the Edinburgh Festival Fringe, where they were spotted by a “Book of Mormon” casting director. Both men fit the physical Cunningham profile: stocky, on the short side (O’Neill is 5-foot-6), with a youthful, kinetic energy. Really the only potential snag was that the last time O’Neill had been in a real singing-and-dancing musical was in high school back in Stamford, Conn., a dozen years ago.

(From Left to Right): Phyre Hawkins, Mark Evans, Christopher John O'Neill in the first national tour of "The Book of Mormon." (Joan Marcus)

Which maybe explains why, as a couple of casting directors looked on, O’Neill butchered the line “Just like Jesus, I’m growing a pair!” by singing, “Just like Jesus, I’m combing my hair!” not once, not twice, but three times before he finally stuck the lyric landing. While he was walking back to his apartment, O’Neill got a call from his mom. She asked him how it went. “I’m so glad it’s over,” he said. When she asked if he thought he’d get a callback, he laughed.

O’Neill nails the line in the show tonight at the Kennedy Center, no problem. His days of rookie flubs are behind him. “Once you get up there, you’re with people you trust onstage and you trust the material,” he said. “And you just kick its a--.”

O’Neill has been on this tour since December but he’s still about as stunned to have landed in this cast as Elder Cunningham was to arrive in Uganda. This is the last place on the planet O’Neill ever expected to be.

The accidental actor

Elder Cunningham begins “The Book of Mormon” as the unlikeliest of success stories. Instead of saying the approved dialogue missionaries are trained to recite, he blurts out, “Hello, would you like to change religions? I have a free book written by Jesus!”

O’Neill didn’t have the most auspicious start, either. Though he had a proclivity for performance in his DNA — his dad is a Juilliard-trained pianist — O’Neill only took to theater in high school because his lousy grades got him kicked off the soccer team. His mom, an eighth-grade teacher with zero tolerance for her son’s poor academic performance, “went to a parent-teacher meeting and came home and said she’d put me in concert choir,” O’Neill said at he sat in his hotel room in downtown Washington.

The choir teacher needed boys to be in the chorus of “Bye Bye Birdie,” and O’Neill figured, why not? “And that was the moment. . . . My whole high-school life was changed around.” He thanks his choir teacher by name in the “Book of Mormon” Playbill.

O’Neill didn’t score a speaking part until senior year, when he played Nicely Nicely Johnson in “Guys and Dolls.” He auditioned for a few college theater programs but, with no real acting training to his name, got rejected from all of them. After graduation, he stuck around Stamford, connected with Valenti, who was a few years older and shared O’Neill’s love of “The Kids in the Hall” and “Saturday Night Live,” and “got super-addicted” to improv.

“That was my goal,” O’Neill said. “I need to do comedy.”

O’Neill was desperate to get out of his parents’ house in Stamford and into New York City, so he and Valenti scraped together the money to go.“I look back now and it’s like, what were we thinking?” said Valenti. “But the chemistry we had kept us going.”

In October 2003, they moved into a 16-by-8 studio apartment behind Lincoln Center. They slept in bunk beds. O’Neill worked a series of “really crappy jobs” in the city: at an ice cream shop, a toy store, a couple of restaurants, as a comedy barker in Times Square. Meanwhile, Valenti would call comedy clubs and pretend to be a manager or an agent, pitching a two-man act. Most nights the duo performed “at the 1:30 a.m. time slot when nobody was there,” O’Neill said.

Valenti remembers “a lot of fights about what kind of direction we wanted to go in… what [is] our niche, and what’s going to make us, brand us?”

“We spent six years trying to figure that out,” Valenti said.

The Chris and Paul Show” is their sensibility distilled to its simplest form: a joke heads in one direction but veers to the left at the last minute, and the sketch snaps shut before the shock fully registers. O’Neill’s self-deprecating way of describing their aesthetic is “stupid and abrupt.”

O’Neill and Valenti toured at some festivals and started taking home awards. The two made their inaugural trip to the Edinburgh Festival Fringe, one of the oldest, largest theater festivals in the world, in August 2011. Despite the unglamorous setting (“The Chris and Paul Show” was “literally performed inside of a cave,” said O’Neill), they won best newcomers at the festival and were invited back the next year: the year a “Book of Mormon” casting director happened upon their act.

After the initial “Book of Mormon” auditions in New York, O’Neill and Valenti both made it to L.A. to try out for Parker and Stone. Valenti stood outside the door at the Pantages Theater while O’Neill auditioned. “My stomach is full of butterflies,” Valenti said. “I hear Chris belt out ‘Man Up.’ And I got chills.”

Valenti didn’t get past the L.A. stage, but O’Neill went back to New York for a month-long workshop. Every day, he and at least a dozen other Cunningham contenders worked with a director, a voice teacher and a music director. And every day was an audition.

It was “mentally grueling,” O’Neill said; two weeks in, more Cunninghams showed up. “Book of Mormon” was casting for multiple companies — Ben Platt, who is Cunningham in the Chicago production, and Cody Strand, Cunningham on Broadway, were at the audition, too — but as far as O’Neill remembers, “none of us knew” that more than one person would wind up with a job.

When he finally got the call offering him a spot on tour, O’Neill signed the contract, with one condition: that he be able to take off April 19, his wedding day. His wife, Jennifer (who took the photo that became O’Neill’s official headshot) stayed in New York where she works at a restaurant software company. O’Neill flew to San Francisco in December 2012. “And it’s been nonstop since.”

“It was a long process,” O’Neill said. “And I wouldn’t change it for anything. If there are people who have overnight success, I’d much rather suffer . . . because you really learn about yourself and discipline, and you pay your dues. That’s why, where I am now, I’m 31 and it happened at the perfect time for me. If it had happened at 21, I’d be like, ‘Oh, that was easy! That’s great!’ Now, I know how hard it is to get somewhere like this.”

A natural-born Elder Cunningham

Mark Evans, the Elder Price to O’Neill’s Cunningham, described a typical night before a show begins: “I’m sat in my dressing room doing my warm-ups or whatever, and all of a sudden I hear a basketball out in the corridor. Or [O’Neill] comes into my room with a mouth organ, or a harmonica.” The man, Evans insisted, “actually is Elder Cunningham in real life.”

In other words, Evans said, “He’s like a child on acid.”

Other soon-to-be missionaries tell Elder Price he’s “like the smartest, best most deserving Elder the Center’s ever seen!” Cunningham, not so much. In real life, “We’re the odd couple,” said O’Neill of his relationship with Evans. “He’s this tall, handsome English guy. . . . And I see how much I can annoy him in every show.”

Evans and O’Neill joined the tour six months in, and O’Neill “was very wide-eyed and green and eager,” said Colin Bradbury, the tour’s dance captain.

“I think he was quite overwhelmed by the whole thing,” said Evans, and has coped with the craziness by “just taking it a show at a time, a city at a time.”

O’Neill agrees: “I’m constantly fighting to make every song work and not screw everything up.” The workload is immense. “There’s no cruise control with this show. . . . It’s 21 / 2 hours of screaming and aerobics.”

Early reviews didn’t pour on the praise for O’Neill’s pipes (a reviewer in St. Louis referred to his “halfway decent vocals”), but there’s a sweetness about him that’s cited almost everywhere. He has a kind of “Put me in, Coach!” charm that gets the audience in his corner. O’Neill has weekly Skype sessions with a vocal instructor and, according to Evans, “His singing has improved immensely. He would be the first to admit that he hadn’t trained professionally as a singer, but now, he’s up there with everybody else.”

What makes O’Neill’s Cunningham click, said Evans, is the humor that got him hired in the first place. “He’s a comedy genius. . . . He’s always pushing boundaries and trying to do new things. And the great thing is, he’s not afraid for something to not work and not land. He’s a brave comedian.”

O'Neill said he’ll definitely audition for more musicals in the future, though “I don’t feel for a second like I made it just because I’m in this show.” He and Valenti still touch base every day, working on sketch ideas and plotting big things for “The Chris and Paul Show.”

Valenti finally caught O’Neill as Cunningham when the tour was in, of all places, the holy land of Rochester, New York, home town of Mormon prophet Joseph Smith.

“It made me so emotional,” said Valenti. “I had nosebleed seats. I was watching him through binoculars. . . . It was just so surreal. I’m looking at everyone around me, and people are laughing at his jokes and just enjoying the show. I just couldn’t get over it.”

“Surreal” is the same word O’Neill uses to describe the past year of his life. For someone who spends 20 hours a week playing a man who always believes, O’Neill still has a hard time believing any of this could really be happening to him.

“Every time I see an advertisement,” he said. “It’s like, ‘I’m in that!”

The Book of Mormon

Through Aug. 18 at the Kennedy Center, 2700 F S. NW,, 202-467-4600.