It happened about 3 p.m. Friday on West Roscoe Street near Damen Avenue, CPD said.
The victim was seriously hurt.
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Police are looking for a white- or silver-colored 2011 to 2013 Toyota Prius C.
Anyone with information is asked to call the Bureau of Detectives - Major Accident Investigation Unit at (312) 745-4521. Tipsters can remain anonymous at cpdtip.com.
Chicago police warned residents not to approach the car if they see it, but to call 911 with its location and direction of travel and a quick description of the vehicle.