If YouTube viewings counted as record sales, Terra Naomi would be on her way to being minted: the video of her eco-protest song Say It's Possible has been watched 2.6m times since June 2006. A home recording featuring the New York songwriter and a guitar, it became a word-of-mouth sensation that led to an appearance at the London leg of Live Earth, a record deal and, tonight, a sold-out ICA headliner.

On stage, Naomi's strong suits are a tenderly expressive voice and a relaxed approach to artist-audience relations. She gets the crowd on-side with quips about having to introduce the drummer - "or he won't play" - and generally behaving as if she were hosting a party for 300 louche buddies in her living room. Her easy manner is undoubtedly the result of having been around the block a few times, with "multiple stints in rehab" under her belt, an experience that has yielded an artist of contradictory parts. There is the confident charmer, urging us to buy her debut album, Under the Influence, and there's the emotional brawler she becomes when she sings.

Ignoring the adage about starting slowly and building it up, she's deep in turbulent waters from the outset. Up Here strides way into Alanis Morissette-ish angst-land, while Vicodin issues the tremulous invitation: "I've got Vicodin, do you want to come over?" Speaking of which, she gives Lou Reed's Perfect Day a queasy, casual treatment that makes listeners feel appropriately grubby, which says something about her powers.

If her tunes weren't surprisingly melodic - Say It's Possible is so clearly a nascent arena anthem that the audience are swaying as one - and if Naomi's voice were less beautiful, this would be the kind of thing that would peak at No 59 in the chart. As it is, the top 10 probably beckons.