I’d be out in clubs with him and it would be like ‘who’s that man? What’s he doing?’

I’d be out in clubs with him and it would be, like ‘who’s that man? What’s he doing?’ He’d go up to all my friends and ask them about me. The piece came out about the whole club thing which I wasn’t even really involved with any more And then he never got me the dress I called him too. ‘So where’s my dress, Jay?’ ‘Oh, my wife just had a baby, I’m working on it…’ You know how much writers get paid on the New Yorker? Hoo!” Journalists! They stitch you up every time.The thing about Chloe is that, in spite of all this ferocious attention – and unlike certain other contemporary icons we could mention – she’s still improbably media-friendly, nattering on about her friends and her folks, and how, on this trip (her fourth) to the coolest city in the world, she plans to take her mom, who is accompanying her, to visit Westminster Abbey and the Crown Jewels. Back home she takes the 45-minute train trip to visit her family in Darian, Connecticut, every week.The shelf-life of icons can be cruelly short, but somehow or other, after over two years of all this, Chloe hasn’t yet exceeded her sell-by date. This month she is splashed across The Face, in one of those nouveau-grunge picture spreads, modelling a ragbag of thrift-shop outfits in a starkly- lit, scruffy bedsit.

The unretouched photos expose a mottled, spotty face and what looks very much like a love bite on the side of her neck. But there’s still something immensely appealing about her.The film roles have been harder to come by: her reputation rests on the slimmest of work. There is Trees Lounge, directed and written (a first outing on both counts) by the actor Steve Buscemi, who has quietly become a cult figure in his own right thanks to a stream of roles in films like Tarantino’s Reservoir Dogs (he was the non-tipping Mr Pink), Jarmusch’s Mystery Train, DiCillo’s Living in Oblivion, the Coen Brothers’ Fargo and Altman’s Kansas City.In Trees Lounge, a low-key drama set in his home town of Valley Stream, Long Island, Chloe (who took the role sight unseen “because I admired Steve so much as an actor and everything”) plays a teenager who takes Buscemi’s boozy drifter for a ride in more ways than one It confirms her as a confident, versatile performer. “I was terrified because it was my first role with professional actors,” she says: the cast includes such heavyweights as Samuel Jackson and Seymour Cassell, a veteran of the late John Cassavetes’ movies. “But at least it gave me a chance to show some range, rather than just walking around crying.”And there will be Gummo, named, for unexplained reasons, after the fifth Marx brother who dropped out of the team to sell lingerie. Written and directed by Harmony Korine, the author of Kids (and Sevigny’s live-in boyfriend), it’s the story of white-trash delinquents and cats which come to a bad end.

Sevigny says she is not supposed to talk too much about it, but explains that she plays “this really poor kooky Middle American girl, white hair and white eyebrows”.But Kids remains her juiciest role. “In Trees Lounge I’m not on screen much, and in Gummo there are no real stars, it’s more of an ensemble film. I think have even less to do than in Trees Lounge.”At the Cannes Film Festival last May she announced three projects in prospect Now, it transpires, they have all collapsed. “We lost the funding – that always happened with independents.” She gets scripts, mountains of them, “mostly stuff by first-time directors”, and ploughs through three a week But nothing good enough to sign up for “Why, you think I should be working more?” she honks “I’m really picky I’d rather work just once a year and make good films. I’m not rushing into anything.”This despite pressures from the entourage she has somehow acquired along the way: an agent in Los Angeles, two in New York, a manager and a publicist “I can’t keep track of everyone,” she says.

“It’s alright, but I don’t feel any one of them really knows what I want to do. They’re all trying to convince that I have to make that one commercial breakthrough film. I wouldn’t mind a big movie, making some money if it was good, but they’re not coming calling for me yet. I’m not bankable enough.”In any case Hollywood, you feel, would not know what to do with her. “Lili Taylor [seen recently in the indie film, I Shot Andy Warhol] has stuck to her guns and she’s still doing amazing work You can make it that route, it just takes longer. And I don’t mind waiting.”And so, in the meantime, Chloe sits and waits, working the festival circuit and hanging out with fellow scenesters in the assorted capitals of the world.