Chelsea and the Metropolitan Police are investigating after an incident of alleged racist abuse during Saturday's Premier League match with Manchester City was highlighted on social media.
Twitter users highlighted a first-half incident when a supporter appeared to abuse City forward Raheem Sterling.
A Chelsea spokesman said: "We're aware of reports and video footage. We will investigate the matter and take the strongest possible action where necessary."
The Met Police said: "We are aware of a video circulating online in which it is claimed racial abuse was allegedly directed at a player at a Chelsea v Manchester City game at Stamford Bridge on Saturday, December 8.
"We will review the footage to determine whether any offences have been committed."
No arrests have been made, the Met added.
Chelsea are seeking to establish the facts of the incident.
Should any offence have been made, a life ban could be handed to the supporter or supporters responsible.