Sky said Hudson-Odoi informed team mate Cesar Azpilicueta, who in turn complained to the referee after the final whistle.
"We can confirm a report of racist abuse directed at one of our players in the final minutes of the match in Kiev from a small section of home supporters," Chelsea said in a statement on their website https://www.chelseafc.com/en/news/2019/03/18/club-statement-on-kiev-incident.
"We wholeheartedly condemn such abhorrent behaviour... We expect UEFA to conduct a fulsome investigation and we will provide full cooperation."
The club said chairman Bruce Buck and club secretary David Barnard had informed the UEFA match delegate of the matter.
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UEFA were not immediately available to comment.
(Reporting by Rohith Nair in Bengaluru; Editing by Christian Radnedge)
