There is more than one artist with this name.

Chelsea are an English punk rock band, formed in London in 1976.

The original line-up was front-man Gene October, guitarist Billy Idol, Tony James (bass) and John Towe (drums, who had come from London SS along with James).

After a few gigs, the other three left October to form Generation X (with Idol later becoming a major star). October then recruited Carey Fortune (drums), Martin Stacy (guitar) and Bob Jessie (bass), with the last two soon replaced by Henry Daze and James Stevenson (who later joined Generation X). This rapid turnover of band-members was characteristic throughout Chelsea's existence, with October the only constant presence.

Chelsea were noted for their socialist politics and the raw emotion of their early live gigs. Their first single, Right to Work, dealing with unemployment, was their most popular song. After spending 1977-78 touring in the UK and overseas, they released their first LP, Chelsea, in 1979. Their second LP, Alternative Hits, was released in 1980. The band released their latest studio album, Faster, Cheaper and Better Looking in 2005. They continue to record and tour.

(There is also a Japanese rock band called CHELSEA.)

Then, there is also-also a early 90's french indie-pop band called CHELSEA, they released three albums : 'Réservé aux clients de l'établissement (1991), Tramway (1992) et 'Nouvelles du Paradis' (1994) and several good singles too.
they were told as 'le meilleur groupe de Tours' at this time ;-)
Disbanded in 1995, they were influenced by bands like JAMES and founding member Emmanuel TELLIER (journalist at Les Inrockuptibles & then Télérama) later created another band called MELVILLE)

Finally, Chelsea was Peter Criss' band prior to joining KISS. Most notably, almost all of Pete's solo tracks started as efforts by Chelsea.