The incident took place in the week ahead of the west London club's trip to QPR, with John Terry set to face trial for alleged racist comments made at Loftus Road in October
British Transport Police said one man remained in police custody in north London after being detained on Sunday, while officers were still looking for other people involved in the incident.
A statement made from British Transport Police before the arrest reads: "We were made aware of the incident on board the 1600 Norwich to London Liverpool Street service.
"It is alleged that some individuals were involved in racist chanting.
"British Transport Police has contacted the individual concerned who made the allegations and an investigation is ongoing."
The alleged incident takes place a week ahead of the club's FA Cup tie against QPR at Loftus Road, with Chelsea captain John Terry set to return to the ground for the first time since his alleged racist comments towards Anton Ferdinand on October 23.
Terry was charged with racially abusing Ferdinand, and is due to appear at West London Magistrates' Court on February 1.
Chelsea promised action against any fans proved to be involved in racist chanting, and a statement on the club's website reads: "Chelsea Football Club is concerned to hear that a small number of fans travelling back by train from Norwich were alleged to be involved in racist chants and comment.
"We are working to help the relevant authorities identify those responsible and will take the strongest possible action should these allegations prove to be true.
"The club, like the overwhelming majority of our fans, strongly believe that all forms of discrimination are abhorrent and have absolutely no place in society."
The west London outfit were earlier forced to condemn supporters' chants about Ferdinand which were heard in their 1-1 Champions League Group E draw at Genk's Cristal Arena on November 1.