Tickets for “Mean Girls” went on sale last week at the August Wilson Theatre, and Tina Fey was there to hand out cheese fries.

The p.r. stunt was, well, cheesy — but effective. Inspired by one character’s all-carb diet, the show gave away nearly 3,000 free cheese fries — I hear they fetched $5 a fry on StubHub — and the box office got a nice big bump.

“It blew the rest of us out of the water,” says a press agent for another show coming to Broadway this season. “But they have Tina Fey, and we don’t.”

Fey’s not in the show, but she’s writing the script, and her name — and the popularity of her 2004 movie — is a big draw, indeed. She joins an exclusive club of writers — Neil Simon, Andrew Lloyd Webber, and “Book of Mormon” team Trey Parker and Matt Stone — whose names alone have sold a lot of Broadway tickets.

Fey, sources say, is working as hard on “Mean Girls” as those others did on their shows. She was at every run-through this week in New York, taking notes, listening to opinions, making cuts, refining jokes.

Buzz from the rehearsal studio is very good, with backers saying Jeff Richmond’s score is as snappy as that of “Mormon” and “Hairspray.” (Richmond is Fey’s husband, but the “30 Rock” theme-song composer’s work stands on its own.)

Director Casey Nicholaw will be on the Acela to Washington, DC, Friday morning to start technical rehearsals for the out-of-town tryout at the National Theatre, where “Mean Girls” runs from Oct. 31 to Dec. 3. Previews at the August Wilson start March 12.

But some “Mean Girls” fans can’t wait that long, and are making pilgrimages to DC for the tryout. (I’m sure George Bernard Shaw had fans, but I doubt they trekked to New Haven, Conn., in 1956 to see his “Pygmalion” become “My Fair Lady.”)

A few highlights from the run-throughs:

• Erika Henningsen, playing newbie Cady Heron, is “better than Lindsay Lohan,” one source says. (The bar’s not high there, but Henningsen is terrific; check out her “Journey to the Past” on YouTube.)

• Taylor Louderman’s playing Regina George, with the kind of delicious evilness Betty Lou Gerson brought to Cruella De Vil in Disney’s animated “101 Dalmatians.”

• Kerry Butler, a standout ever since “Hairspray,” performs her three roles with such flair that she may steal that Special Tony Award away from Bruce Springsteen.