Police said the two-car crash happened just before 3:30 p.m. in the 300-block of West 35th Street, near Guaranteed Rate Field.
Video from near 35th and Shields shows officers chasing the suspect, a 23-year-old man, after police say he drove into oncoming traffic, hitting another car.
Three people in the suspect's vehicle, a 2-year-old girl, a 6-year-old girl and a 19-year-old woman, were transported to local hospitals in good condition.
They are all expected to be OK.
The driver is charged with reckless driving and child endangerment.