CPD said a man approached a male passenger from behind and punched him in the face about 1 p.m. last Tuesday at the Fullerton Red, Brown and Purple Line station.
Police said the initial attack happened on a train, and the suspect ran off.
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The male passenger who was punched and a female passenger chased the suspect, and the suspect hit the female passenger with a long chord, police said.
The passengers were injured in the incident, police said.
The suspect remains at large and is described as a 30- to 35-year-old man, who is 5-feet, 9-inches to 5-feet, 11-inches tall, with short black hair and a black beard, police said. He was last seen wearing grey pants, white socks and black open-toed sandals.
Anyone with information is asked to call public transportation detectives at 312-745-4447 or submit an anonymous tip at CPDTIP.com.