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Chester FC said it was "ashamed" to be associated with those behind the chant - which was made during the club's National League North match against Hereford on Tuesday night.
The chant made reference to Letby being from the town of Hereford.
The 33-year-old was jailed for life last month after being found guilty of murdering seven babies and attempting to murder six others while working at a neonatal unit at the Countess of Chester Hospital.
Letby - the most prolific child serial killer in modern British history - was sentenced to 14 whole-life orders - meaning she will never be released from prison.
Chester FC's vice chairman, Jim Green, said: "The club condemns the appalling chant heard during our match with Hereford.
"We are ashamed to be associated with anyone responsible for the chant.
"It is reprehensible behaviour and demonstrates a deeply concerning lack of compassion, understanding and decency.
"The impact of Lucy Letby's horrifying crimes continues to be felt throughout our community and the collective thoughts of the football club, our staff and supporters remain with the families and loved ones of the babies."
Mr Green said the club would review CCTV footage to identify those involved and take "appropriate action".
Last month, the Crown Prosecution Service (CPS) updated its guidance in relation to "tragedy-related abuse" - when fans chant or gesture offensive messages about disasters or accidents involving players or fans.
They warned fans faced being banned from games if they mocked tragedies such as the Hillsborough disaster, the Munich air crash or the Bradford City fire.
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The move was backed by the chief executives of the Football Association (FA), Premier League and English Football League.
Chief Constable Mark Roberts, of the National Police Chiefs' Council, also welcomed the effort to tackle the "mindless and vicious chanting that unfortunately a minority of supporters engage in".