A bullet hit the bill of the baseball-style hat the paramedic was wearing, police said. He was unhurt.
CPD said a suspect in an older model green Buick fired shots at the hospital in the 1900-block of Ogden Avenue just after 10:30 p.m. and then sped off.
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The shooting, which shattered glass at the hospital, appeared to result in a chaotic situation.
It was not immediately clear what led up to the shooting.
About 10 minutes later, two men, 28 and 31, were outside when they were shot by someone in a vehicle about 10:25 p.m. in the 2300-block of West Warren Boulevard, police said.
The older man was shot in the chest and arm, and was taken to Stroger, where he died, police said.
The younger man was shot in the right heel, and was also taken to Stroger, where he was in good condition, police said.
Chicago police said there is no one in custody, and Area Three detectives are investigating.
This is a developing story; check back with ABC 7 Chicago for updates.
Sun-Times Media contributed to this report.