"Welcome to Belfast," sighs the assistant chief constable, grimacing apologetically as he hands DS Stella Gibson (Gillian Anderson) a bulging case file. "I've done 28-day reviews before, you know," she tuts, flicking regally through a wadge of blotchy mortuary snaps and false-lead suspect profiles. "Not here you haven't," continues Constable Roflz, scowling significantly out of the window. "Things are different here."

He's not wrong. Things are different here. Very different. So different, in fact, are things in The Fall (Monday, 9pm, BBC2) that it's probably easier to list the things that it's not, if only to give ourselves something to cling to when the more familiar, context-y stuff begins to shift, the floor gives way and everything starts to slide inexorably into a deep, knotted, bilious swamp of … differentness. So, some things that The Fall is not: a sitcom, a musical, a cooking show presented by men in distressed leather moccasins, a panel quiz, a thing about whales, a police procedural. Yes, it follows the hunt for a serial killer, but the serial killer is revealed within the first few minutes, peeling off his balaclava in a victim's flat, no less, before eating an orange and burying his beard in a pair of her pants. It's not a detective drama, either. Not really. Yes, we pound along after prickly DS Gibson as she quietly humiliates stupefied subordinates and draws important red circles around photos with her big Met-issued marker pen. Yet as much screen time is devoted to her wholly unlikely quarry: one Paul Spector (Jamie Dornan, excellent), a mild-mannered grief counsellor who enjoys jogging and jolly family days out when he's not strangling trainee solicitors or scribbling pictures of his clients' knockers in his notepad while they try to tell him about their dead children.

The Fall is an exercise in unexpectedness. That it's also one of the best things to have appeared on the BBC in years is almost by the by: this, it booms in its enormous, barrel-lunged Irish brogue, is how to make a relentlessly original, consistently gripping, vast-brained five-part psychological thriller with a gimmick (in essence: let's devote equal attention to the hunter and the hunted) that never feels like a gimmick, but rather the perfect means of exploring the banality of evil, the nature of obsession, and the niggly-squirmy minutiae of everyday, common-or-garden murder. Phew. Created by Prime Suspect 2 writer Allan Cubitt, it's all rather brilliant.

The plot, then: a young Belfast architect has been murdered and the local plod is up to its squeaky rubber truncheon in confusion. Enter, tutting, Gillian Anderson, an Arctic roll in a pencil skirt. "Where's that coffee?" she blurts smirkily before promptly linking the case with an earlier unsolved murder, telling everyone to tuck their shirts in, and launching a task force determined to stop the killer before he strikes again. Meanwhile, somewhere across the city, Paul Spector is kissing his doting wife goodnight and preparing for his next murder.

The sense of creeping unease mounts. A teenage babysitter flirts innocently with Spector ("I've had my braces removed!"). His young daughter begins to have nightmares. His son asks him what he's got in his bulging backpack. Horrible things happen, horribly. Nothing is as it seems. Gibson may have all the markings of the heroic maverick-about-town – the tart one-liners, the non-existent home life, the crisp-white-shirts-as-metaphor-for-obsessive-fastidiousness – but she's as glib, icy and detached as Spector. Then, at the end of the first episode, she says something to a colleague that catapults our preconceptions into a nearby thicket. But that's The Fall all over. Just when we think we've got this hunter/huntee lark sussed, it whisks the chair from under us, leaving us with our bumcheeks clenched in horror. If there's a more original anything this year, I'll eat my squeaky rubber truncheon.