N’Golo Kante struck the winner after Ander Herrera had been sent off in the first half.
It was a feisty encounter at Stamford Bridge with managers Jose Mourinho and Antonio Conte also clashing on the touchline.
Ander Herrera red card: Did Man Utd ace deserve to be sent off?
Tue, March 14, 2017
Do these pictures prove Manchester United ace Ander Herrera shouldn't have been sent off against Chelsea?
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Did Ander Herrera deserve to be sent off for these two fouls on Eden Hazard?
Manchester United fans have been accused of homophobic chanting
Antonio Conte and Jose Mourinho clashed on the touchline
United saw their hopes of winning a treble ended on a frustrating night a Stamford Bridge.
And The Sun claim their fans are now being investigated by police for homophobic chanting aims at Chelsea.
Supporters have been accused of singing “Chelsea Rent Boys” during the game.
The FA are looking into a complaint made by a Chelsea fan who was told by police what he had heard was “unacceptable.”
Chelsea players celebrate N'Golo Kante's winner
A United spokesman said: “The club aims to work closely with Chelsea to identify anyone believed to have engaged in discriminatory behaviour at the game and will follow the terms of our Official Sanctions Policy if necessary.
“In addition, we will liaise with Chelsea to determine any activity to discourage such behaviour before the next fixture.”
Any fans found guilty of the chanting will face anything from a three-game ban to indefinite suspension.
FA rules and ground regulations forbids abuse based on sexual orientation in keeping with criminal law.