The man tried robbing the Bank of America branch at 2337 South Cicero at around 10 a.m., according to a spokesman for the Town of Cicero.
The attempted robber did not display a weapon or imply he had one, but did give the cashier a threatening note, the spokesman said.
The man fled the bank without taking any money from the clerk, who notified police immediately.
Police have released surveillance images of the suspect. Anyone with information is asked to call the Cicero Police Department at 708-652-2130 or the FBI at 312-421-6700.