Says Chloe: "My manager sent me the script and I read it, and ... (pause) actually, no - that's not what happened at all. What am I talking about?" And she lets rip with her notorious honking sea-lion laugh, a laugh she emits often, as though nothing, least of all an interview, deserves to be taken at all seriously.
Chloe, 22, is the Kids kid: the naive youngster who contracts Aids from a one-night-stand in Larry Clark's controversial movie about New York teens (so controversial, in fact, that a major chain of UK cinemas refused to show it). Inevitably the film's commercial performance failed to live up to the aggressive hype. But it helped launch Chloe's cover-girl career.
By then she had already clocked up a couple of appearances in pop videos, by Sonic Youth and the Lemonheads, a few gigs as a "spokesmodel" (whatever that means) for designer labels like Miu Miu. But her main, and perhaps most embarrassing achievement was to have been the "It Girl", subject of a seven-page splash in the New Yorker written by the novelist Jay McInerney: a sort of Young Fogey's Guide to Generation X.
"They were asking around and people mentioned my name, I don't know how or why - I guess I knew a lot of scenesters," Chloe says of how she came to be singled out for this dubious honour. "Jay said to me, 'Yeah, it'll be really quick, I'll just go out with you a couple of nights,' and I said, 'OK, I'll agree to do it if you get me this dress that I really want, a Helmut Lang dress that you couldn't buy at the time'. He said, 'not a problem, I know so many people in the industry I can get it free'.
"So he ends up following me everywhere for a month. 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. Pending a terrific acting role, she would quite like to deploy her unerring and instinctive clothes sense by working as a costume designer (a function she performed on Gummo). But, she says, "I've been talking to my agents about it but they always say, 'if you do that then people take you less seriously as an actress'." One wishes her well: it would, after all, be a great pity if Chloe wound up famous for being famous, slipping gently down the celebrity B- and then C-lists into the "whatever happened to..." columns, instead of becoming what she almost certainly has it in her to achieve, a unique and quirky acting talent.
'Trees Lounge' opens on 14 March.