While you definitely don’t need a car in Chicago, it can be useful depending on which area you’ll be living in. If you’re close to a bus or train station, you’ll be able to get around the city without a vehicle at your disposal. And some buses and trains will take you outside of the city if you want to visit nearby places.
However, it’s much faster to drive in most areas of Chicago. While traffic can be an issue, avoiding rush hour and the downtown area will make it much easier to travel by car in the city. Sometimes, having a car at your disposal can cut transportation times in half.