Exeter are working closely with police after former England international Ugo Monye accused a supporter of racist abuse following Sunday's Gallagher Premiership match against Gloucester.
The 40-year-old ex-Harlequins player, who was working as a pundit, claimed he was subjected to the "most blatant racism" he has heard as he was leaving Sandy Park.
Exeter have apologised to Monye and say CCTV footage which captured the incident has been passed to Devon and Cornwall Police.
"Exeter Rugby Club have been working closely alongside Devon & Cornwall Police following the reported incident of racial abuse," read a club statement.
"We would like to say a big thank you to the huge number of people who have been in contact with the club with statements and information regarding the incident.
"We know that this behaviour is not representative of our fans.
"Exeter Chiefs have a zero-tolerance policy for behaviour of this kind, and we have acted as quickly as possible to ensure that this has been dealt with following the advice of all appropriate authorities."
Monye wrote on X, formerly known as Twitter, that one supporter running through the crowd repeatedly shouted a racist insult.
He added: "Disgraceful. Not a single person said a word, challenged or even reported it.
"He walks off after a mild scuffle and fans are now telling me 'We're with you' B******S you're with me. You weren't with me when you saw and heard the most blatant racism I've seen from a supporter at a live game. So fed up."
Sky Sports News have contacted Devon & Cornwall Police for comment.
The Rugby Football Union said in its own statement on Monday: "We are appalled by the racist abuse Ugo Monye faced following the Exeter Chiefs game against Gloucester.
"Ugo is a great champion of rugby, inclusion, and diversity; he has our full support. Racism cannot be accepted in our sport.
"Rugby authorities, clubs, fans, players and volunteers must all act consistently and without tolerance to any form of abuse of discrimination."
Premiership Rugby has also offered support to Monye and urged anyone with information to come forward.