In recent weeks there have been more than 20 reported incidents where shoppers and businesses have spotted counterfeit money, mostly £20 notes, in the city centre.
Now police are hoping to work with the public to remove the money from circulation.
Det Sgt Barry Brown, of Chester Inner Neighbourhood Policing Unit, said: "Counterfeit money is a serious problem and it usually hits the open market as a result of some earlier form of criminal activity – often relating to drugs.
"Of course the most common handler of counterfeit money is the innocent member of the public or shopkeeper who are handed notes as they go about their daily business.
"We are working extremely hard to take these dodgy notes out of general circulation and want people to be on their guard when using paper money and to check every note they receive.
"All Bank of England notes have a number of security features, such as raised text, metallic thread, microtext and holograms, and while some fakes can be very close to the real thing none can replicate all of the features.
"Another indication that notes are counterfeit is ink staining.
"This is often used to mask imperfections in the print of the fakes and any stained notes should be treated with extreme caution."
Anybody who thinks they may have received a fake note should check the security features against those listed on the Bank of England's website www.bankofengland.co.uk/banknotes/security.
If they are still unsure they should take the note to a police station. You will be given a receipt for the note which will then be sent to the Bank of England for testing. If it is genuine you will be reimbursed in full.
Anybody with information should contact Cheshire Police on 0845 458 0000 or Crimestoppers anonymously on 0800 555 111.
The full article contains 335 words and appears in Evening Leader Chester newspaper.