Chelsea have appealed for help in identifying the fan who made an alleged racist gesture during Wednesday's defeat of Manchester United.
A picture of the alleged incident was published in several national newspapers, prompting Chelsea to announce a club probe.
A formal complaint has further been made to the Metropolitan Police, who have begun a criminal investigation.
A statement released by the force on Thursday read: "Police have received a complaint regarding alleged racist behaviour at Stamford Bridge (on) Wednesday, October 31.
"An investigation has been launched. There have been no arrests and enquiries continue."
A statement from the west London club read: "Chelsea Football Club can confirm we are investigating an incident involving a member of the crowd at (Wednesday) night's game against Manchester United.
"The club will be examining all available footage and asks anyone who can identify the individual to contact the club.
"Chelsea FC is committed to removing all forms of discrimination and if we have sufficient evidence we will take the strongest possible action, including supporting criminal prosecution."
Chelsea are also looking into the behaviour of the visiting United supporters after flares were lit in the away end and one fan ran onto the pitch.
The matter comes at a sensitive time for Chelsea having lodged a formal complaint with the Football Association against referee Mark Clattenburg for using "inappropriate language" towards midfielder John Obi Mikel. That matter is also being investigated by police.
Chelsea have been involved in a series of race-related issues over the past year.
In March the club banned for life a supporter who admitted racially abusing former player Didier Drogba.
The most high-profile incident concerned captain John Terry, who is currently serving a four-match ban after being found guilty of racially abusing QPR defender Anton Ferdinand by the Football Association.