CHICAGO — In the final few minutes of “Billie Jean,” the new play with Broadway aspirations at Chicago Shakespeare Theater, we follow Billie Jean King and her spouse, Ilana Kloss, the South African former tennis player. King, one of the most extraordinary living Americans and once (frankly, still) one of the most famous women in the world, came fully out of the closet relatively late in life, and the scenes involve King’s loving but traditional Southern California parents accepting the lesbian couple.

Those moments are deeply emotional and, quite frankly, beautiful enough in their simplicity to bring a tear to the eye. Chilina Kennedy, the Canadian star who plays King, is finally allowed a chance to breathe and Callie Rachelle Johnson, who plays Ilana (among others), is one of those performers capable of creating a character to whom one inherently warms. King has come home in all the ways we all crave and the gravitas and challenges of her journey feel at once familiar and extraordinary. In a world seemingly bereft of heroes and heroines, these last few minutes send the audience out on a genuine high.

I wouldn’t normally talk about the end of a show like this, but this hardly is a spoiler for any tennis fans who have followed King’s career. More importantly, this script and production would be so much better if more scenes took their time to land emotionally and felt the same way.

Biographical shows about very famous, and very impressive, living people are tricky. The writer inevitably wants to please and hail the subject, who holds the keys to her own life, having been there. As we’ve seen with many Broadway jukebox biographies, even if the subject doesn’t want a hagiography (and I can’t imagine that the famously honest King did), that doesn’t mean she won’t get one. There’s also commercial motivation: No one coming to a play about Billie Jean King is looking for something that does not celebrate her achievements.

So it’s easy for the authorial voice to blur with the subject, and that is what happens here, a bit too much. Supporting characters, many of whom remain overly one-dimensional, are seen through a singular lens.

On some levels, that’s fair enough. We can read whose name is on the marquee. And why not celebrate the struggles and triumphs of such an icon?

Given that King is now 81 years old, it’s also likely that generations of Americans are less than fully aware of all she achieved and I can see mothers, especially, taking their daughters to this show and saying, “See?” The piece is also a celebration of the multi-decade LGBTQ struggle, and of the LGBTQ community as a whole, especially since it includes King’s full-throttle support of the pioneering transsexual player Renée Richards (Murphy Taylor Smith), tacitly distinguishing King from, say, Martina Navratilova on that issue. All of the above are valid reasons for a piece of biographical theater.

But I also think plays, even plays about a person as virtuous and courageous as King, also have an imperative to challenge and surprise their audiences. You don’t get other points of view here on anything, at least not beyond the appearance of various stereotypical obstacles to King’s progress. So when the play, say, posits the Australian player Margaret Court mostly as a villain, one cannot help but wonder what she would have had to say, given the chance. The same is true of Larry King (Dan Amboyer), who is a confusing and underwritten presence here, kinda supporting the heroine one moment and behaving like the classic controlling dude the next, so as to fit the overall narrative in which his influence must be vanquished for full self-actualization. I wonder what he would have said, too.

Plus, human lives like this one are long, and they can feel that way when plays precede chronologically. “Billie Jean” sets itself the task of exploring its subject from girlhood through emergent doubles accomplishment, through her astonishing list of singles titles at Wimbledon, where she thrived, to her complicated but abiding marriage to Larry, through the famous “Battle of the Sexes” match with Bobby Riggs to the scandal involving King’s relationship with Lenne Klingaman’s wacky Marilyn Barnett (who filed a palimony suit against King in 1981), to King’s work to create the Virginia Slims tournament (and by extension the WTA tour), to how the media treated her to her admirable philosophies of life to her impact on Venus Williams (Courtney Rikki Green).

Along the way, it heralds many of King’s views of sports and life, including her conviction, rare among professional athletes of all stripes, that “pressure is a privilege.”

King’s life has, to say the least, been amply documented. For decades. So for those of us who have followed tennis, we already know about her astonishing 39 Grand Slam titles and her unstinting advocacy for women’s tennis, especially the need to persuade the tennis establishment that women deserved to have a place to play, equal and fair compensation, and to be recognized and understood not just for their looks or as amateur curiosities but as some of the world’s greatest professional athletes. And, of course, we also know what King achieved in tennis also (eventually) crushed barriers to women in other sports from golf to soccer.

“Billie Jean” tells its laudatory story very capably, thanks in no small part to a very energized and fluid production from director Marc Bruni. The show does not feature actual tennis (beyond a few stylized arm movements and sound effects), nor does it get into the tennis weeds at all; “Billie Jean” actually never really explores what made King so good at the game besides chronicling her determination and love of winning. Some sense of her formidable technique surely would help round out the picture. The show also glosses over her first singles title, which seemed strange to me, but then there’s a lot to cover in such a life. The battle with Riggs also zips by, presumably since the show well knows it already was the subject of an excellent movie.

At times, it feels like you are watching a staged Wikipedia entry, frankly, given all the narrative interjections from the eight-person ensemble, not all of which are needed. But at others, playwright Lauren Gunderson’s skills with poetic language really kick in, the text takes more risks of style and form and Kennedy, who is superbly cast in this difficult role, handles everything anyone hurls her way with aplomb.

I’m sure many of King’s fans will love this piece, which is set on a revolving tennis court set designed by Wilson Chin, but I hope the next draft deviates a little more from the straight race through an incredible American life and sits longer with the beating heart of its most human of subjects.

That, after all, was Billie Jean King’s actual secret weapon.

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'BILLIE JEAN'

3 stars

When: Through Aug. 10

Where: Chicago Shakespeare’s Yard Theatre on Navy Pier, 800 E. Grand Ave.

Running time: 2:20

Tickets: $73-$134 at 312-595-5600 and chicagoshakes.com

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