In the 61 years since the Tony Awards began, only four women have won Best Director honors: Julie Taymor (“The Lion King”) and Garry Hynes (“The Beauty Queen of Leenane”) in 1998, Susan Stroman (“The Producers”) in 2001, and Mary Zimmerman (“Metamorphoses”) in 2002.

This Sunday night at Radio City Music Hall, Anna Shapiro is poised to become the fifth.

For her work on the Pulitzer Prize-winning “August: Osage County,” Ms. Shapiro has already won the coveted Drama Desk and Outer Critics Circle awards for best direction of a play. All of which means that a 42-year-old director from Chicago is on the cusp of capturing a Tony for her Broadway debut.

It’s all a bit overwhelming to the publicity-shy Ms. Shapiro, who gives the impression she would much rather be teaching a class at Northwestern University (where she heads the graduate directing program) than walking red carpets. “It’s not that I don’t have personal aspirations,” she said over a cup of coffee in a Chelsea café, on the day the Tony nominations were announced. “But I don’t think about [the awards] that much.”

Indeed, if there is a pattern to Ms. Shapiro’s career, it’s a tendency to veer off the kind of path that typically leads to Tony nominations. After graduating from the Yale School of Drama in 1993, she left the East Coast for her native Chicago. These days, “about 99%” of her work in the theater is focused on developing and staging new, unproven plays. And earlier this year, she turned down a prestigious job — artistic director at the American Repertory Theatre in Cambridge, Mass. — in large part because she didn’t want to leave her students at Northwestern. Moreover, she freely admitted to having “a genuine mistrust of wide appeal.” The often-harrowing “August,” she noted, is “much lighter, oddly, than most of the work I do — and much more emotionally lush.”

Yet even living 800 miles from Broadway, maintaining her resolute focus on new work, Ms. Shapiro has occasionally been thrust into the New York limelight. In 2006, her off-Broadway production of “The Pain and the Itch” generated tremendous buzz. Then came the juggernaut of “August,” directed by Ms. Shapiro for Chicago’s Steppenwolf Theatre Company, where she is an ensemble member.

The show’s Broadway transfer (with original cast intact) opened in December to almost universal acclaim, and Ms. Shapiro was cited in a sizable share of the rave reviews. “Anna D. Shapiro … has pieced together every component beautifully,” Eric Grode wrote in the December 7 New York Sun.

It wasn’t merely that Ms. Shapiro — in collaboration with the play’s much-lauded cast — had made the 3 1/2-hour saga of a fractured Oklahoma family fly by. She had also staged it with uncanny brilliance, populating the play’s iconic three-story, cross-sectional dollhouse set with all the simultaneous action of a sprawling family briefly reunited under one roof — without her audience ever feeling uncertain of where to look next.

As befits a member of the Steppenwolf ensemble, a collaborative repertory company that is more focused on achieving bare-knuckle psychological realism than apportioning credit, Ms. Shapiro tends to downplay her own contribution to the phenomenon of “August.” With all the affection of someone who has been affiliated with Steppenwolf for more than a decade (and directed 17 of its productions), she declines to specify her role in generating the remarkable interplay between the characters. She will only say that her 14-member cast is “the most amazing group of people put together in a room that I have ever seen in the theater. And I am a lover of the theater.” When pressed, she admitted that “on a self-important day” she sees her handiwork in “how the people move, the simultaneity of the action” — the way the house “feels alive.”

Not that Ms. Shapiro is some shrinking violet. A tall, striking woman with an intense gaze and a low, throaty voice, she projects confidence and no-nonsense intelligence. (At drama school, a classmate once jokingly referred to her as “the truck stop waitress who will one day run American theater.”) And she has thrived in the rough-and-tumble atmosphere of Steppenwolf, whose storied membership includes powerhouse actors such as John Malkovich, Laurie Metcalfe, Gary Sinise, Jeff Perry, and Joan Allen.

“One time, very early on, John Malkovich took me out to dinner just to tell me how much he hated a play of mine,” Ms. Shapiro said with a smile. Steppenwolf, she acknowledged, may have earned its early reputation for having a macho culture, but “the women were macho, too” — herself included. “I never felt limited at all at Steppenwolf because I was a woman,” she said.

It was through Steppenwolf that Ms. Shapiro’s relationship with the writer of “August,” Tracy Letts, developed — though she first directed him “in a little theater in Rogers Park that I think had 45 seats.” At the time, he handed her his play “Killer Joe,” which she thought was “disgusting.” “Clearly,” she laughed, “I have a real eye for talent.”

Years later, when Mr. Letts brought her “The Man From Nebraska,” her response was warmer. She directed it at Steppenwolf in 2003, impressing Mr. Letts enough that he brought her an early draft of “August.”

“I remember the feeling the night I read it, which was, I have the best life ever, that people will hand me plays like this.”

Mr. Letts’s draft already specified that the play was to take place in a sprawling house. Ms. Shapiro was game, but the house as written, in her estimation, “was not physically possible.” With her set designer, she went to Mr. Letts and laid it on the table: There had to be fewer rooms. Mr. Letts’s reply flummoxed her. “Great,” he said. “You do it.”

“So we cut out about four or five rooms, and I just figured out where things could happen and kept the audience as close as I could,” Ms. Shapiro said.

The resulting multiroom set posed a challenge, but it was a familiar challenge, Ms. Shapiro insisted. “In any play, you have to create a hierarchy of ideas that are running at the same time,” she argued. “This was just a kind of literalization of that. And to show that so clearly was a great thing for a play about a family. Because the hell of family is that you’re having to live alongside these people who are simply not having the same experience that you are having.”

Within the confines of that stuffy, claustrophobic house, Ms. Shapiro strove to have the audience “feel like they’re watching something they’re not supposed to be watching.” To that end, she took care to rein in the actors’ impulse to “hand things out to the audience.” In rehearsal, both before the opening and in her periodic trips to New York since, she has often told the actors, “I’m gonna kill your fun now.”

She hasn’t killed all their fun. Along with Ms. Shapiro, three of the show’s actors — Deanna Dunagan, Amy Morton, and Rondi Reed — are up for Tony Awards on Sunday, as are the play’s set designer, Todd Rosenthal, its lighting designer, Ann Wrightson, and Mr. Letts, for Best Play.

But even if she wins, don’t expect Ms. Shapiro to change her stripes. Her next project is another Chicago production with a close-knit ensemble — she’s co-directing a revival of “Our Town” with Jessica Thebus for the Lookingglass Theatre Company. “I think it’s gonna be really fun for us,” she said. “And I hope it’s fun for the audience,” she added, with a wry laugh.