“Empathy isn’t your strong suit.” That’s Amanda (Olivia Cooke) addressing her friend Lily (Anya Taylor-Joy) in the sleek, withering psychological chiller “Thoroughbreds.” By that point her criticism will strike you as either laughably redundant or outrageously hypocritical, since Amanda is, if anything, even more removed from the normal spectrum of human emotions than Lily is.

The bond between these two human icicles is at the pitch-black heart of writer-director Cory Finley’s debut feature, a mean-girls noir that ponders the logistics (and occasionally, the ethics) of a little murder between friends. The person they want dead is Lily’s stepfather, Mark (Paul Sparks), who is the bane of her existence, though his wealth accounts for why that existence looks so enviable, at least on the outside.

Much of the movie unfolds inside the suburban Connecticut mansion where Lily lives with her gormless mother (Francie Swift) and her loathsome stepdad. The camera surveys the grounds in long, elegant tracking shots, allowing us to take in the handsomeness of the decor but also the spaces that seem to stretch endlessly between the characters, isolating them in a sea of empty, wasted privilege.

“Thoroughbreds” is thus a story about two bored, amoral youths who decide to turn distant fantasy into cold-blooded reality; it’s “Double Indemnity” or “Rope” with a female millennial spin. The title, a reference to the prize horses that are stabled in this upscale neighborhood, is also a metaphor that the story drives home in its less subtle moments: What happens when two well-groomed, hot-blooded mares begin acting up?

It’s a testament to the filmmaker’s skill that the answers are worth sticking around for. Spending 90 minutes with a pair of teenage sociopaths may not sound like your idea of entertainment, but these two are a peculiarly nasty pleasure to be around, in part because they seem utterly indifferent to either your presence or your approval.

Finley, a New York-based playwright, knows how to write dialogue that tingles with menace even as it drips with self-awareness, but he also has a fluid compositional sense that keeps “Thoroughbreds” from lapsing into staginess. The blend of formal suavity and deadpan domestic absurdism at times reminded me of the work of the director Yorgos Lanthimos (“The Lobster”). Cooke, in particular, would fit in right alongside the experientially stunted young sisters in “Dogtooth,” Lanthimos’ brutal 2010 portrait of an unconventionally conventional family.

Home turns out to be similarly where the horror is in “Thoroughbreds.” It’s also the perfect place for Lily and Amanda, under the pretext of tutoring sessions, to renew their long-dormant childhood friendship. Both have been recently ostracized, for very different reasons: Lily was expelled for plagiarism, jeopardizing her college prospects. Amanda is undergoing psychological evaluation after committing a violent act against a horse that makes “Equus” look tame.

“I don’t have any feelings, ever,” Amanda says early on, and whether she’s making an observation or a statement of principles, Cooke’s frighteningly affect-free performance honors it to perfection. Being utterly immune to emotions like joy and sorrow — not just her own, but also those of the people around her — has given Amanda a ruthless clarity of insight. She cuts through phony layers of small talk and penetrates everyone’s psychological defenses, Lily’s included. She’s a chillingly perceptive monster.

Lily, played by Taylor-Joy with some of the same touching, troubling vulnerability she brought to “The Witch,” isn’t quite as emotionally bereft as Amanda. She’s still capable of rage, most of it directed at Mark, with his brusque, authoritarian manner (to say nothing of his insufferable juice cleanses and 24-7 rowing workouts). But when it comes to mimicking Amanda’s detachment and manipulating circumstances to her advantage, Lily turns out to be a dangerously quick study.

The threat of violence churns beneath nearly every frame of this poised and coolly disturbing movie, but Finley’s diabolical sense of mischief is held in check — and in some ways amplified — by his discretion. The story is rife with lethal intentions and nasty dealings, and the tension is no less acute for the fact that the worst of what happens is left to the imagination.

“Thoroughbreds” builds to a climactic sequence, immaculate in its framing and sound design, in which suspense, horror and poignancy commingle in one extraordinary single take. It’s with both admiration and a tinge of regret that I say I wish the movie had ended there.