Attempts on Her Life, about a mystery woman named Anne, is not an easy play to produce—and it's almost impossible to get right. The idea that a new theater company would try it as its first-ever production is impressive. Even more impressive: This company, the Horse in Motion, has chosen to perform it as an immersive experience that spans three floors of the creaky old University Heights Center, where audience members are guided from room to room to watch its loosely connected scenes performed out of order. On paper, it sounds like a bizarre and wildly ambitious opportunity for failure. Amazingly, they pull it off.

Written in 1997 by British iconoclast Martin Crimp, Attempts on Her Life looks more like a thought experiment than a play, with 17 scenes and no defined characters. The script has only dashes to indicate when a new person speaks ("—They're making love in the man's apartment." "—Doing what?" "—Making love"), meaning each scene could be performed by one actor or 10 and set anywhere from a tea shop in Cairo to a spaceship orbiting Mars. It's the kind of oddball challenge young artists with more passion than discipline might fantasize over, then turn into meaningless jelly. But director Bobbin Ramsey and her small army of actors and designers have filled its nebulous parameters with crystallized characters and images that are both intriguing and unnerving.

The production begins when audience members walk into a cavernous wood-paneled room, order drinks at the bar, and listen to a young woman playing piano and singing "Sex and Candy," "Gold Dust Woman," and other ominous love songs. Phone messages from people in Anne's life are piped over loudspeakers: her mother saying she got the postcards but can't send any more money, someone saying her "vehicle" has arrived in the showroom, a jet-setting lover blowing her off, someone praising some artwork, a Czech voice telling her to "leave the device in a small truck at the back of the building," and several threats ("I'm going to fuck you up the ass. With a broken bottle. And that's just for starters").

Then the tour guides—mine was a charming young man named Ben wearing eyeliner, a neatly trimmed beard, and sleek black boots—escort small groups through the building. We sit in at a living-room fundraiser with wine and cheese, where a bourgeois do-gooder couple tells us what happened in an idyllic, exotic valley ripped apart by an atrocious civil war. We walk into a dark bathroom where hooded cult members come out of the stalls and lead us to a young girl on a floor, reading fashion magazines in her sweatpants, who they transform into a sex symbol. One room is turned into an art show, full of artifacts of the artist's many attempts to commit suicide (bloody glass hanging like a mobile, pill bottles, suicide notes, a rifle), and we overhear our tour guides fiercely debating the work. We walk down a big staircase and look through a small window, watching soldiers rough up prisoners. We hear about a young woman's trip through the world of pornography and then maybe politics.

The only humor in this world, with its Anne-shaped hole in the center, is gallows humor. One of the liveliest and most grimly funny scenes takes place in a hallway, where three people in a stereotypical Euro-Gypsy getup speak Russian (translated by our tour guide) and try to sell us a car called "the Anny," pantomiming its amenities: Besides air-conditioning and automatic windows, "there are no filthy Gypsies in the Anny... no one is ever dragged from the Anny by an enraged mob... the backseat is never made slippery by semen... there is no room in the Anny for the degenerate races."

Crimp wrote Attempts on Her Life as intentionally bewildering—Anne is a Patty Hearst–style revolutionary, then an art star, then a porn star, then a suicidal schizophrenic, then a refugee, then a "good woman" with a wholesome rural family who happen to be militant white supremacists. Perhaps it's a portrait of America seen through a British lens of admiration and disgust. It has some flab, which Horse in Motion cleverly dispenses with: One short scene is texted to our phones, another is hidden in an installation of Anne's chaotic bedroom, typed out and tucked into drawers.

The greenness of these young actors peeks through occasionally—some uniquely thespian overenunciation, the occasional panting performance—but these concerns are hardly worth mentioning given the enormity of what they've achieved. It's been a few years since a young new theater company burst onto the scene, making people sit up and take notice. Attempts on Her Life is a bracing hello. I'm already impatient to see what the Horse in Motion will do next.