The American Century Theatre’s update of the FDR-era Broadway smash Hellzapoppin’ kicks off with a terrible joke: An announcer on the P.A. who thinks he’s there for another show throws a fit when he sees the copy he’s supposed to read. It’s forced. It’s painful. It’s not funny.

Then — Mercy! — a man in a gorilla suit shows up. Man in gorilla suit = crazy hilarious. But if you don't agree, then perhaps one of the roughly 4,587 other sight gags, pratfalls, or ill-advised musical numbers coming at you in the next two-and-a-half hours may be more to your taste. Or make you laugh, anyway, since “taste” and this sort of comedy don’t have much to do with one another. If you loved the Zucker Bros. movies like Airplane! and its many descendants — or especially the original Muppet Show — then you won’t want to miss this opportunity to see where the no-laugh-too-easy, no-pun-too-egregious, more-is-more school of laffs aplenty had its genesis.

Ole Olsen and Chick Johnson were the vaudeville duo that starred in the original Broadway version, which ran for more than 1,400 performances between 1938 and 1941, a record at the time. Bill Karukas and Doug Krenzlin appear as Olsen and Johnson here, respectively, acting as emcees for the evening’s revels. (Krentzlin also had a hand in updating the script, along with director Jack Marshall and several of his fellow cast members.) They’re marvelous company, groaning their way through the show along with us. It overstays its welcome, to be sure, and there are a handful of recurring gags that don’t pay off nearly well enough to justify their protracted setups. But unless you're a complete stick-in-the-mud, the production’s eagerness to please and willingness to offend will eventually win you over all the same.

The cast is huge and their ability varies wildly, but everyone gets points for fearlessness. A few are especially praiseworthy for their Herculean ability to stick with sorta-funny bits that go on so long that they eventually become funnier — or funny again — by virtue of sheer audacity. Esther Covington is one of them. Hundreds of musicians have covered “Eleanor Rigby,” but few if any ever forgotten its lyrics so memorably. Ron Sarro, meanwhile, who plays the Little Blue Man and a bunch of other, equally creepy roles, clearly has no capacity for embarrassment, which in a show like this is a kind of super-power. And as the Great Howdidi, an escape artist who seems to have oversold his abilities, John Tweel will have you praying he never succeeds.

Hellzapoppin’ is playing Thurs..-Sat., with 8 p.m. evening performances and 2:30 p.m. Sat. matinees through Aug. 18 at the American Century Theatre. Order tickets ($23-$29) by email at info@americancentury.org or call (703) 553-8782 to order by phone.