Everton are investigating reports of homophobic chants during Saturday's win over Chelsea at Goodison Park.
The Merseyside club released a statement on its website on Sunday.
The club statement read: "Everton is working in conjunction with Kick It Out and has commenced an investigation into homophobic chanting reported during Saturday's Premier League game against Chelsea.
"Both the Club and Kick It Out have received reports of a homophobic chant being aimed at Chelsea's fans by a small section of the home crowd.
"Homophobia has no place within our stadium, our Club, our community or our game. The Club strongly condemns such behaviour and is carrying out a thorough investigation which will include liaison with Merseyside Police."