Police said shots were fired around 5:40 a.m. in the 3100-block of West Palmer Square in the city's Logan Square neighborhood.
No one was injured by gunfire, but police said a car crashed into three parked vehicles at that address and the driver fled the scene.
Witnesses told police they saw another vehicle, which appeared to be following that car before the crash.
At least three people were killed in three other shooting incidents in Chicago early Wednesday morning.
A man was shot and killed while sitting in his car in the city's Fuller Park neighborhood around 12:45 a.m. A woman was shot in the head while fleeing an attempted robbery in Chicago's Englewood neighborhood around 2 a.m. Three people were shot - two fatally - in the city's West Garfield Park neighborhood around 3:40 a.m., before the SUV they were riding in crashed into a pillar supporting the CTA Green Line tracks.
This surge in violence occurred despite CPD adding more officers and emotional pleas for peace from Mayor Rahm Emanuel and city faith leaders earlier this week. Authorities said 66 people were shot - 12 fatally - in Chicago other the weekend.