Rim, 46, was shot at about 6:40 a.m. Thursday when he was a passenger in a car in the 4100 block of West Diversey Avenue on the city's Northwest Side.
A Nissan Rogue, with unknown Illinois license plates, pulled up and, after a verbal exchange, someone in the SUV shot Rim in the head through his open passenger-side window, police said.
The Nissan Rogue has tinted windows and is missing a front license plate.
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After the shooting, the SUV drove westbound on Diversey Avenue and then southbound on Kostner Avenue.
Rim, who lived in South Barrington, died at Mt. Sinai Hospital.
Police are investigating and working with a possible road rage motive.
Anyone with information about the shooting is asked to call Chicago police's Bureau of Detectives - Area North at 312-744-8261.