A report on a Jewish website claimed that one supporter was left "disgusted" by the chants, and complained to stewards at Vicarage Road.
He was moved to the family enclosure "for his own safety" after taking pictures of the alleged perpetrators.
Chelsea have since released a statement which condemned any behaviour which "shames the club".
"Anti-Semitism has no place in our club, football or wider society," it read. "Anyone found guilty of anti-Semitic language or behaviour will face action from the club, including bans, and will be asked to attend equality education courses.
"We welcome the fact that Chelsea fans have reported this behaviour, which shames our club.
"We ask all fans who share our vision for a game open to all to report any kind of discrimination they witness or experience.
"We will be working closely with the police and Watford to identify those responsible and will take the appropriate action."
The club have now launched an investigation into the incident along with Watford and the police.
Chelsea last week began a 'Say No to Anti-Semitism' campaign as part of the Building Bridges initiative.
Club owner Roman Abramovich was joined by high-profile individuals from across the Jewish community and by antisemitism campaigners at a gathering before last week's match against Bournemouth.