Like Scripture, show business often seems touched by the hand of Providence. A few years ago, Trey Parker and Matt Stone, the creators of the gleefully subversive animated TV series South Park, went to see the cheeky, Tony-winning puppet musical Avenue Q. Over a drink afterward, Robert Lopez, one of the show’s authors, mentioned that he had been kicking around ideas for a musical about the Mormon prophet Joseph Smith. Stunned, Parker and Stone said that they, too, had always wanted to write a musical about Smith—and, hey, why didn’t they all do it together? This month, the seed planted at that encounter is finally bearing fruit as Broadway gets ready for The Book of Mormon, a faith-based extravaganza of jaw-dropping obscenity, hair-raising blasphemy, and irresistible good cheer that may just be the funniest musical of all time.

Parker and Stone are no strangers to show tunes. Their score for the 1999 movie South Park: Bigger, Longer, and Uncut, which includes the Oscar-nominated “Blame Canada,” won them such lofty admirers as Stephen Sondheim. And though they’re famous for scabrous attacks on religious hypocrisy, they’ve always had a soft spot for Mormons, whom they tend to depict as dopey and credulous but really, really nice. “Mormons are so Disney and Rodgers & Hammerstein to begin with that it makes perfect sense for them to break into song,” Parker says. “That’s why, in many ways, this feels like a traditional musical. You’re being cheesy and corny and all—but that’s who Mormons naturally are.”

The plot focuses on a missionary odd couple—Elder Price (Andrew Rannells), a golden boy with a sense of destiny, and Elder Cunningham (Josh Gad), a tubby loser with a desperate need to be liked—who are sent to Uganda, where they quickly discover that, as one of them puts it, “Africa is nothing like The Lion King.” “You’ve got these little nineteen-year-old white boys from Utah with their attitude of ‘We know how the world works,’ ” says Stone. “Then they get sent to a place filled with poverty and starvation and AIDS and all sorts of superbad shit, and suddenly none of what they’ve learned is of any use at all.”

From the opening number, in which a parade of clean-cut missionaries in black slacks and white shirts ring doorbells and try to spread the good word, it’s clear that The Book of Mormon is not just a spoof but a real musical. Both its tuneful score and the witty, exuberant choreography, by Casey Nicholaw (Spamalot), who codirects with Parker, make fun of the conventions of musical theater even as they celebrate them, with echoes of classic shows from The Music Man to Fiddler on the Roof (an elaborate nightmare sequence in hell, complete with Adolf Hitler, Jeffrey Dahmer, and a Starbucks).

At a staged reading of the show last summer, a few songs hit such heights of offensive hilarity that they left audience members literally gasping for breath—a “Hakuna Matata”–style production number, in which disease-ravaged villagers lift their spirits by telling God what He can do to Himself (and in which orifices), comes to mind.