Chelsea's modern reputation as a centre of innovation and influence originated in a period during the 19th century when the area became a veritable Victorian artists' colony: artists as well as writers lived and worked here. A particularly large concentration of artists existed in the area around Cheyne Walk, where the pre-Raphaelite movement had its heart.
Chelsea became prominent once again as an artistic centre, Bohemian district and hot spots for young professionals in the 1960s, the so called period "Swinging London" . King's Road became the definition of style and fashion and both the Beatles and the Rolling Stones lived in the neighbourhood.
Original article (modified) source: Wikivoyage, where you find useful information about Chelsea. Creative common licence