Can a show hew so closely to its past glories that it becomes a gilded museum piece? That’s a question whipped up by the razzle-dazzle Broadway revival of “Chicago,” which bowed Tuesday at the Orpheum Theatre in Minneapolis for a week’s run.

Not that the 1975 John Kander-Fred Ebb musical is some hermetically sealed diorama. Far from it, this “Chicago” is a smooth and slick machine, studded with zestily entertaining showstoppers and a whole lot of pizazz. The show also harks back to the original meaning of the world “jazz”: It’s infused with sex.

Still, it sticks so close to the Brechtian vision that Bob Fosse had 43 years ago — an approach re-created by Fosse’s partner Ann Reinking in choreographing the 1996 revival that has essentially been touring for 22 years — it feels a touch antique.

The touring show’s director, David Hyslop, and choreographer David Bushman have re-created Reinking’s re-creation of Fosse. Call it an echo of an echo. And why not? It’s worked so well that the “Chicago” franchise has become a billion-dollar industry.

It made the subject of murder entertaining and fun. And its depiction of a corrupt judicial system and a corruptible press are themes that resonate today.

The staging is like a vaudeville show set in a courtroom, with Robert Billig’s brassy, energetic orchestra at center stage on risers, flanked by chairs where the performers sit between numbers. Clad mostly in clingy black sheer fabrics and leather — a kind of bondage-chic that “Chicago” shares with another Kander and Ebb musical, “Cabaret” — the actors take turns telling us the Jazz Age story of women murderers behind bars in Chicago.

Both Roxie Hart (Dylis Croman), a chorus girl, and Velma Kelly (Terra C. MacLeod), a jazz singer, have killed for passion. And they share a defense attorney, Billy Flynn (Jeff McCarthy, looking Joe Biden-esque), a silver-tongued precursor to the Johnnie Cochrans of the world who orchestrate media coverage of sob stories to keep their his off the gallows.

The single honest person is Roxie’s sappy mechanic of a husband (Paul Vogt), whom she uses and abuses throughout. Though he wins our sympathies, he never gets any redemption in the show.

The principals are smooth and affecting in “Chicago.” Croman is by turns coquettish and full of guile as Roxie. As an actor, dancer and singer, she’s lyrical and graceful, nailing her character’s many moods. Her song “Roxie,” a fantasy about being surrounded by male performers, is a highlight.

Croman’s smooth performance has a counterpoint in MacLeod’s Velma. An athletic dancer with short-cropped hair, MacLeod is streamlined and all business. She’d be right at home as a Bond love interest (or villain). And she holds the spotlight, especially on “Cell Block Tango.”

The production is, in fact, studded with gorgeous performances. Jennifer Fouché brings down the house with “When You’re Good to Mama.” And “We Both Reached for the Gun,” in which Billy Flynn treats Roxie like a ventriloquist’s dummy, is theatrical gold.

While this “Chicago” has small updates throughout, at heart it remains a throwback to the work that Fosse (and Reinking) did years ago. No matter. If museums are respected as repositories of great art, history and culture, why can’t a musical do the same?