Enemy” opens Friday at Sundance Cinemas. R, 1:30, three stars out of four.

It happened to me. It was 1995, and I was backpacking through Europe. At the Czech Consulate in London, while waiting to get a travel visa to go to Prague, I looked across the crowded waiting room. Slouched against the far wall was a man who looked exactly like me.

I didn’t go up and talk to the guy – I’m guessing physical resemblance isn’t the conversation starter that you might think it is — but always wondered what that guy’s deal was, what sort of life he had led. And felt a little tingle at the odds that I had found him, halfway around the world.

Denis Villeneuve takes that tingle and expands it into full-on dread in “Enemy” a heady and disturbing thriller that reteams him with Jake Gyllenhaal. If their previous collaboration, “Prisoners,” was a major-label studio album, than “Enemy” is the EP put out on their own label — rougher, less conventionally satisfying, but with a nervy spirit all its own.

Gyllenhaal plays Adam Bell, a Toronto professor sleepwalking through his life, repeating the same history lectures in class by day, glumly coupling with his bored girlfriend (Melanie Laurent) at night. On the advice of a colleague, he rents a movie from his local video store (yes, his local video store — I told you this movie was weird) and finds it to be a dumb comedy.

But standing in the background of one scene is an extra who looks exactly like Adam. Fascinated, Adam searches the Internet to find out that his doppelganger is Anthony St. Clair (also Gyllenhaal), an arrogant actor with a gorgeous apartment and a beautiful pregnant wife (Sarah Gadon). Gyllenhaal uses subtle shifts in posture and expression to play the two different men, one who thinks the world is his to conquer, the other who feels it barely has room for him.

As Adam starts stalking Anthony and trying to learn more about his life, Villeneuve builds an enveloping atmosphere of tension, all the more tense because we’re not exactly sure why “Enemy’ is making us nervous. What would happen if Adam and Anthony meet? Would they wink out of existence, like the matter/anti-matter twins of that one old “Star Trek” episode. Or would one seek to dominate the other, to steal their life from them? And which twin has the more to fear, the more to lose, from the other?

The screenplay by Javier Gullon, based on Jose Scaramago’s 2004 novel “The Double,” offers no easy answer, including a final image that’s a flat-out “WTF?” moment. Instead of turning on the lights, “Enemy” follows Adam on his descent into darkness, the Toronto skyline often presented in a poisonous ochre haze, the score a jumble of ominous strings and sudden percussion.

The obvious influence for this sort of film is another Toronto filmmaker, David Cronenberg, who also found evil lurking behind the seemingly banal face of the city. But “Enemy” isn’t an exact twin of a Cronenberg film, either. In fact, none of Villeneuve’s films (which include the searing Middle East thriller “Incendies“) look much like each other. But they all keep us on edge, a little nervous that somewhere in their dark corners, we’ll recognize ourselves.