The female driver was reportedly speeding when she lost control and struck several concrete barriers just before 3:30 a.m.
No Burnham police officers were hurt. Emergency crews responded to the pin-in crash, and the driver was transported in critical condition to Christ Hospital in Oak Lawn with leg injuries.
It's unclear why police initiated the chase and why the driver was trying to evade the officers.
The car had Indiana plates and a baby seat in the back, but the driver was alone.
"I looked out the window and I heard the siren and seen a squad car and got out here and I seen the car wedged down here on the end and an officer was assisting the vehicle," said a man who lives in a trailer outside the crash site.