Storage Locker Information at Union Station Chicago
22.25" high x 12.5" wide x 32.28" deep
$4 for the first hour
$12 for 3 hours or more (24 hours max)
35.25" high x 18" wide x 32.28" deep
$6 for the first hour
$16 for 3 hours or more (24 hours max)
If none of these options work, then your best bet is to head to one of the museums that offer coat check services and offload your bags there to explore the city. The Art Institute of Chicago near Grant Park is a good one and has a large coat check/baggage storage area costing just $1 per item. This of course means you are lugging your stuff to and from the museum though...