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Chelsea have the fifth highest average all-time attendance in English football and regularly attract over 40,000 fans to Stamford Bridge; they were the fifth best-supported Premiership team in the 2005–06 season, with an average gate of 41,870. Chelsea's traditional fanbase comes from working-class parts of West London, such as Hammersmith and Battersea, from wealthier areas like Chelsea and Kensington, and from the Home Counties. In addition to the standard football chants, Chelsea fans sing songs like "Carefree", "Blue is the Colour", "We all follow the Chelsea" (to the tune of Land of Hope and Glory), "Ten Men Went to Mow", "Zigga Zagga", "Hello! Hello!" and the celebratory "Celery", with the latter often resulting in fans ritually throwing celery.

Chelsea do not have a traditional rivalry, in the manner that Liverpool and Everton, or Arsenal and Tottenham Hotspur do. The club's nearest neighbours are Fulham, but they are not seen as big rivals by Chelsea fans, because the clubs have spent most of the last 40 years in separate divisions. A 2004 survey by Planetfootball.com found that Chelsea fans consider their main rivalries to be with (in order): Arsenal, Tottenham Hotspur and Manchester United. Additionally, a strong rivalry with Leeds United dates back to several heated and controversial matches in the 1960s and 1970s, particularly the FA Cup final in 1970. A more recent rivalry has grown with Liverpool following several clashes in cup competitions. In European competition, Chelsea's biggest rivals are Barcelona, with the two competing to be among the best sides in Europe and having played in some highly controversial matches in the UEFA Champions League in recent seasons.
During the 1970s and 1980s in particular, Chelsea supporters were long associated with football hooliganism. The club's "football firm", originally the Chelsea Shed Boys, now known as the Chelsea Headhunters, were nationally notorious for violent acts against hooligans from other teams, such as West Ham United's Inter City Firm and Millwall's Bushwhackers, both during and after matches. The increase in hooliganism in the 1980s led chairman Ken Bates to propose an electric fence to deter them from invading the pitch; the proposal was rejected by the GLC. Chelsea's hooligan element were revealed to have links with neo-nazi groups such as Combat 18, and other far-right or racist organisations including the British National Party. Since the 1990s there has been a marked decline in crowd trouble at matches, as a result of stricter policing, CCTV in grounds and the advent of all-seater stadia.