Go to the ticket counter. "Ticketing" on this map.
http://www.chicagounionstation.com/map_concourse.html
You'll arrive on one of the southern platforms (could be any of them).
The one time I checked baggage at CUS I went to the Ticketing counter. When I got up to the window and said I wanted to check a bag I got yelled at by the helpful Amtrak employee for being at the wrong window. There is a single baggage check only window at the far right (if I remember correctly) of the Ticketing counter, which has its own line. Try to just check baggage at a CUS ticketing window and you will be yelled at.
Yes, she *could* have checked my bag, she had all the facilities for checking bags and did check bags for people who were buying tickets, but you see, I already had my ticket so I was at the wrong window and had to be yelled at and sent away.