Ever since the state of Georgia enacted the nation’s most generous tax breaks for film and TV production, Atlanta has become what’s often considered the “Hollywood of the South.” But for all the movies that use the city as a backdrop, few actually center it as a dynamic metropolis worthy of its own mythology. (The list basically begins and ends with Donald Glover’s eponymous FX series and a handful of reality shows.) The Peacock miniseries “Fight Night,” adapted by creator Shaye Ogbonna (“The Chi”) of the 2020 podcast of the same name, is a welcome change of pace from the status quo, using one fateful night in the 1970s to explore Atlanta’s rise as a center of black culture and prosperity — even if some of the architects of that rise weren’t exactly savory characters.

But “Fight Night,” subtitled “The Million-Dollar Heist,” doesn’t lure viewers in with the promise that it will, according to its title card, “show something that really happened.” The eight-episode limited series boasts one of the star-studded casts this side of “Big Little Lies,” led by Kevin Hart and Don Cheadle as two men stranded between worlds. Hart plays Gordon “Chicken Man” Williams, a small-time businessman hoping to impress black mob boss Frank Moten (Samuel L. Jackson) by hosting an afterparty for Muhammad Ali’s comeback boxing match. Williams leads a double life punctuated by his two romantic partners: his wife Faye (Artrece Johnson), with whom he goes to church every Sunday, and his mistress Vivian (Taraji P. Henson), with whom he engages in all sorts of secret activities, mainly illegal gambling. Cheadle portrays J.D. Hudson, a detective who began his career as one of the first black recruits to join the Atlanta Police Department after integration. Hudson’s white colleagues are predictably prejudiced, while most black Atlantans regard him as, to quote the show’s fictional version of Ali (Dexter Darden) when Hudson is assigned to his security detail, “a supervisor.”

When a gang of armed robbers crash Chicken Man’s party and rob Frank and his fellow mob bosses, both protagonists are under immense pressure: Chicken must clear his name before the victims exact some vigilante justice, and Hudson must contain the violence before it spirals out of control. The fight with Ali was intended to generate positive PR for the up-and-coming city, a trajectory Chicken hoped to capitalize on by pitching Frank as a “Black Vegas.” Instead, the robbery he took the fall for has generated all the wrong headlines.

“Fight Night” sits at the intersection of several TV trends with diminishing returns, from the madcap war for true-crime IP to an escalating arms race for star power. But Ogbonna and co-showrunner Jason Horwitch have delivered an engaging, briskly paced series that makes the most of a packed roster. “Fight Night” lacks the detailed minutiae of more compelling Nixon-era entries like “The Deuce”; its soundtrack of perfunctory cuts, from the Temptations’ “Papa Was a Rolling Stone” to Darondo’s “Didn’t I,” reflects its expansive approach to world-building. Still, “Fight Night” compensates for its expert blueprint (true story + big names = win) with nuanced ideas and engaging performances.

As Williams, Hart — also an executive producer — walks a fine line. The comedian neither recycles his stock, goofy persona nor compensates for it with a full-on dramatic turn. As a role, Chicken Man is well-chosen because he’s an inherently ridiculous figure, fighting for Frank’s approval while carrying out myriad schemes in the hopes of getting ahead. But with his life, and that of his family, on the line, Chicken’s desperation takes on a more existential tone. It’s a subtle extension of Hart’s range, not a forced one.

Nearly every other actor fares just as well. Henson, reunited with her “Hustle & Flow” and “Empire” collaborators Craig Brewer (who directs half the season) and Terence Howard (who plays Frank’s ally, Jersey boss Cadillac Richie), gets a full box of toys to play with, from a rollicking dance sequence to a midseason makeover to some Cookie Lyon-esque animal prints. Jackson’s Frank is calmer and more cunning than some of his other roles, though that trademark explosive anger simmers just below the surface. Cheadle gradually eases Hudson into a frenzy, from learning to respect and encourage a “loudmouth” Ali to teaming up with Chicken on an off-the-books mission to track down the heist mastermind.

Our window into the heist operation is McKinley “Mac” Rogers (Sinqua Walls), a shell-shocked Vietnam vet who signs up to pay for a better place so he can share custody of his nine-year-old daughter. (Walls isn’t as famous as some of his costars, but his work helps lend the series a sense of tragedy.) The third episode of “Fight Night,” directed by Tanya Hamilton, plays out almost in real time as Mac’s crew takes and gradually loses control of a house party full of high-profile victims. Such tense, immersive work compensates for the overreliance elsewhere on distinctly vintage-coded devices like split-screen.

“Fight Night” continues to focus on the life-or-death stakes that help the show maintain its momentum. But its characters are united by a purpose beyond mere survival. “I’m trying to be something bigger and better,” Henson’s Vivian cries. “Aren’t you?” Frank, like countless gangsters before him, wants to go legit; Hudson wants to make a difference; Chicken wants to make something of himself, whatever that looks like. “Fight Night” makes these desires compelling enough to use them as a proxy for an Atlanta on the brink of national fame, driven by a black elite. Selling that connection is a feat in itself.

The first three episodes of “Fight Night” are available to stream now on Peacock, with remaining episodes airing weekly on Thursdays.