I don't know about Chicago, but we're off to New York in a couple of weeks and I had the same concern. On the NYC transportation website it says:
"Drivers of yellow medallion taxicabs and for-hire vehicles and their passengers, are exempt from laws regarding car seats and seatbelts. Keep in mind, the TLC encourages everyone in the vehicle to buckle their seatbelts while riding in a cab. There are no Taxi and Limousine Commission rules regarding this, as it is a State exemption. Passengers with children are encouraged to bring their own car seats, which the drivers must allow passengers to install."
I'd be super nervous travelling around a major city without our LO in a car seat. Luckily his seat clicks into the pushchair frame so we'll be taking the whole lot across the Atlantic with us. A pain I know but better safe than sorry.