Lyric discussion by Atman 

Cover art for (I Don't Want to Go to) Chelsea lyrics by Elvis Costello & the Attractions

Chelsea is a district in London full of trendy boutiques that has been a mecca for arty Bohemians. In the swinging 60's, it was the epicenter for mod fashion. In keeping with the general themes throughout the album "This Year's Model," the song could be an expression of distaste and repulsion for the fashion world.

In the 70's, Chelsea (in particular a boutique called "SEX" on King's Road) started to cater to the growing Punk/New Wave trend. Since EC was writing the song about this time, it could be interpreted as a resistance to being lumped in with the Punk/New Wave movement. He resisted those labels throughout his career, so the song could be an expression of independence from that.

Chelsea could also refer to a retirement home for military veterans. Given the recurring themes of anti-military and anti-fascism throughout EC's work, the song could be interpreted as a resistance to being drafted and sent off to war.

@Atman In his biography, EC says it is about his father, who was living in Chelsea at the time and going through a hippie phase of his life, so Elvis didn't want to see him.

They patched it up over the years and had a pretty good relationship.