You will need to collect your luggage in order to go through Customs at O'Hare- then as you come out of customs you can deposit it for onward flights. Is your connecting flight on the same airline?
Allow an hour or so to get through Customs and Immigration and then you can set off. If you walk out any of the doors marked 'Ground Transportation' you will find outside several shuttle services- Mears Shuttle, Supershuttle, there are many. For around $19 per person you get a shared van ride to any of the downtown hotels. You may have to wait for him to fill up with passengers, and you might go to a couple of hotels on the way,but this is the cheapest if you are just one passenger. Just ask him to drop you at the Swissotel on E. Wacker Drive- (I just give that hotel as an example,if you have another in mind...ok) Once you get there- if you're facing the hotel front door, then walk down the hill to your right towards the bridge (1 minute)and then walk to the right (NORTH) crossing the bridge- now you are on North Michigan Avenue (the Miracle Mile)which has everything you need to amuse you for a couple of hours or more. Shops/restaurants,skyscrapers to gawp at, go up the Water Tower for great views over Chicago - the Chicago river for a quick boat ride, or the Lake (Michigan) to wander around. Take the FREE trolley ride up and down the avenue- look for the sign in the front window that indicates it is the free one- there are some that charge for a tour.
If there's more than one passenger I would just get a cab from O'Hare, ask him to drop you anywhere on NORTH Michigan Avenue- (you don't want South) oh, outside Virgin Megastore or Saks will be central, it is a long long road. Taxi runs around $40 plus.
I would be sure to get a taxi back- you don't want to wait around for shuttle services- taxis are plentiful,just raise your hand and hail a cab on the street-yellow cabs are everywhere....do not need to book ... .Need to be back allowing plenty of time to get through traffic- O'Hare is about 15 miles or so outside town- then of course Security screening etc- depending on time and day it gets crowded,you probably know that
You can also get a subway train, for around $3 per person each way, but honestly I wouldn't mess with it in case of confusion with stops, delays etc,given that your visit is very limited.
Chicago is a fabulous town, hope you get to see some of it.