Before songs by the creative masterminds behind ABBA, Benny Andersson and Björn Ulvaeus, took center stage in the most beloved jukebox musical of all time, the two suffered a belly flop on Broadway.

“Chess,” a show that teamed the duo with the lyricist Tim Rice — known for his collaborations with Andrew Lloyd Webber, among them “Jesus Christ Superstar” and “Evita” — began its life as a concept album before taking theatrical form on the West End in 1986. 

Two years later it transferred, like a number of ill-conceived projects that have appealed to critics and audiences across the pond, to New York, where it promptly closed after 68 post-preview performances and some lacerating reviews.  

“Chess” has nonetheless remained something of a cult favorite, particularly for its shiny, power-pop score, which includes the rap-infused “One Night in Bangkok,” a hit single four decades ago, and several anthemic ballads. 

In 2003, the musical returned for a one-night benefit performance that featured Josh Groban in his Broadway debut, along with Sutton Foster, Raúl Esparza, and other big-voiced troupers.

Now “Chess” has re-emerged for a proper run, boasting a brand new book by Danny Strong, known for his work on TV’s “Empire” and “Dopesick,” and a cast led by three stars who also share famously healthy lungs: Lea Michele, Aaron Tveit, and Nicholas Christopher. 

The production reunites Ms. Michele with Michael Mayer, the celebrated director who guided both her breakout turn in the original staging of “Spring Awakening” and her triumphant comeback three years ago in his revival of “Funny Girl.”

Ms. Michele is cast here as Florence Vassy, the chess strategist — or “second,” as they’re apparently called — who is advisor and lover to Mr. Tveit’s character, Freddie Trumper, an all-American bad boy/genius who is identified at one point as a “deranged narcissist.” 

As the show opens, it’s 1979, and both Freddie’s world-championship title and his relationship with Florence, who’s described as “brilliant and beautiful,” are about to be challenged by a Soviet player, the “sad and suicidal” Anatoly Sergievsky.

These appraisals are delivered by The Arbiter, introduced in previous versions as the international chess official overseeing the competition between Freddie and Anatoly in Merrano, Italy. 

In Mr. Strong’s version, the character is also a narrator and an omniscient, wisecracking commentator. 

“Welcome to the first, and depending on how this goes, last, Cold War musical,” he quips at the beginning.

The new libretto burdens The Arbiter — adroitly played and brightly sung by Bryce Pinkham, another musical theater veteran — with other obvious nods to more recent developments, including stupid jokes mocking Robert F. Kennedy, Jr. and Joe Biden. (At the preview I attended, the first got the predictable, self-congratulatory round of applause while the latter drew more of a mixed response.)   

Anatoly’s coach, a KGB operative named Molokov — like the cocktail, with one letter changed — provides a cartoon villain, as does a CIA operative, lest anyone accuse the creators of sharing Freddie’s anti-Russian bias. As Molokov, Bradley Dean rubs his hands together and rolls his Rs with a vengeance, while Sean Allan Krill’s American agent is by design stiffer, with a shock of yellow hair.

I doubt that many of the enthusiastic fans surrounding me at the Imperial Theatre had come to check out these supporting players, or Mr. Strong’s revamped book, for that matter. 

The big draw of this “Chess” is the chance to see the three leads — all of them very attractive, as glamorous photos in ads and on the playbill cover emphasize — and to hear them sing the show’s melodrama-packed score to the rafters.

On these points, at least, the revival doesn’t let anyone down. Mr. Tveit and Ms. Michele make their entrances dressed to kill in sleek black costumes, designed by Tom Broecker, and pose with the studied aloofness of models at a shoot; Mr. Tveit slouches a bit, perhaps to better project Freddie’s sexy irreverence.  

Standing against David Rockwell’s spare, stylish set, often lit by Kevin Adams in blue and Soviet-red neon — what, you were expecting something more subtle? — the stars then tear into the vocal showcases they’ve been assigned. 

“You cannot oversing it,” Mr. Christopher said of the score in a recent Times interview, but his crooning, however technically impressive, can challenge that proposal; at one point during the recent preview, he held a note so long that I feared he might pass out. (The crowd loved it, of course.)

Mr. Tveit, given a brasher character, takes full advantage, bringing rock-star bravado to Freddie’s songs and his lines, which are weighed down by a background involving emotionally abusive parents. 

Florence, too, has suffered — born in Hungary, she was torn from her own mother and father in 1956’s attempted revolution against the Soviet-backed government — but Ms. Michele’s acting and singing are a little more measured; tunes such as “Heaven Help My Heart” and “Someone Else’s Story” flatter her lovely tone and accommodate her disciplined belting.    

This “Chess” ends, in fact, with a twist that puts Florence’s story front and center. Perhaps this production is best appreciated as a vehicle for Ms. Michele — though fans of her costars, and the unabashedly over-the-top numbers revisited here, shouldn’t be disappointed.