In its dissection of conventional family structures and gender roles, Cloud 9 feels like the most timely play of 2016—a remarkable accomplishment given that it first appeared in 1979. Suggesting, if not declaring, that the choice between celibacy and heteronormative monogamy is a yoke of colonialism that even the most ardent colonialists only pretended to abide, Cloud 9’s first half feels pointed and provocative. To call the play a sex comedy would diminish it, though that’s exactly what it is—albeit one in which a character observes mid-orgy, “You can’t separate economics from fucking.” The line comes in the play’s quieter, more searching second half, which contemplates the eroded certainties of patriarchy and empire and asks: Now what?

Of only this much can we be sure: It’s really fucking funny. Studio Theatre’s crisp, haunting new production is director (and longtime Shakespeare Theatre Company honcho) Michael Kahn’s first Caryl Churchill—surprising, given the director and the playwright are contemporaries—but Studio’s sixth. They’ve produced her work as often as anyone else’s, but it’s been a while. Their prior Churchill, the meditation-on-cloning A Number, was more than a decade ago.

Churchill’s work has only grown more daring since Cloud 9, but this warhorse, her first big trans-Atlantic hit, is still progressive in form and intention. Act One is set in an unnamed African nation under British rule. Act Two takes place a century later, in 1979 London—though the three characters who recur from the first act have aged only 25 years. (“I felt the first act would be stronger set in Victorian times, at the height of colonialism, rather than in Africa in the 1950s,” the playwright explained in 1983.) Technology, politics, and social mores are shifting more rapidly than our fragile vessels can bear.

But we are not our bodies. The casting willfully scrambles age, race, and gender—not at random, but in specific configurations, per the script. In Act One, Edward, a little boy whose affection for dolls troubles his parents, is played by Laura C. Harris, an adult woman. Betty, Edward’s mother, is played by Wyatt Fenner, a man. Joy Jones, a young black woman, plays Betty’s elderly white mother-in-law, while white actor Philippe Bowgen embodies Joshua—a native boy who has forsaken his blood relatives and considers himself the adopted son of colonial administrator Clive. (Clive is a white man played by a white man, John Scherer).

Again, Churchill did not simply encourage directors to discount physical characteristics; she said explicitly that a white man should play Joshua, a black woman should play Maude and so on. There’s less stunt casting in Act Two—though Bowgen now plays Cathy, a little girl who adores toy guns—suggesting the lifting of Victorian strictures now permits us to play the roles to which we’re suited, rather than the ones to which we’re… bodied.

The inciting incident of Act One is the arrival at Clive and Betty’s well-appointed home of two guests, the ex-Army adventurer Harry Bagley (a game Christian Pedersen) and acerbic widow Mrs. Saunders (the great Holly Twyford). To his imperious pal Clive, Harry seems the very model of masculinity, a corrective influence for his effete boy, Edward. In fact, Harry’s appetites are voracious: for Joshua (“Shall we go into the barns and fuck?” he enquires, as though offering a drink), for Betty, and even for the kid. Clive is too busy ordering Joshua around and going down on Mrs. Saunders (who hilariously chides herself for permitting it while it’s still happening) to notice. Meanwhile, Edward’s governess (also Twyford) pines for Betty. If you can’t be with the one you love, honey, love the one you’re societally permitted.

The root of their unhappiness in Act Two isn’t so easily summarized. Victoria, who was present only as a doll in the first act, has grown up to become Laura C. Harris, and is now a mother herself. She’s coupled with Martin (Pedersen), a dim writer working on “a novel about women, from the woman’s point of view.” Her big brother Edward (played by Scherer) yearns for more commitment in his relationship with Gerry (Fenner), who feels smothered and prefers quickies with strangers on the subway. Jones plays Lin, a young woman drawn to Victoria whose brother is a soldier stationed in Belfast — the last and nearest outpost of a shrunken empire. Twyford assumes the role of Betty, now a middle-aged widow trying to get used to doing things for herself. It’s improved her sex life, at least, as we learn in a monologue that would be striking in its tenderness even if it didn’t follow two hours of (largely) bawdy comedy.

Their liberation isn’t complete: Edward, a gardener, is still in the closet to his employers at least, for fear of losing his job. “I think I’m a lesbian,” he says, while consensually feeling up his sister. The second act signals its fast-forward to the late 20th century by having the cast line up to reprise the imperial fight song that had opened Act One, only to drown them out with “Good Times, Bad Times,” the first track on Led Zeppelin’s debut album. The tune was already a decade old in ’79. But as a signifier for British appropriation of African music by way of one of its former colonies, you could hardly do better.

The play runs through Oct. 16 at Studio Theatre. $20–$85. 1501 14th St. NW. (202) 332-3300.