I would book the later flight and try to standby on the earlier... it will feel better if you happen to make the earlier flight and get home versus feeling awful that you're forced to sit around Ohare for 3+ hours.
My $0.02? "Own" that 3 hour time difference and pick something unique to Chicago to do for some of it... go up the Willis tower, see the beans, or go to a museum or something. Take a breath and slow life down for an afternoon.