Agree w/ Kevin, although we get less reports from Union Station than we do from Ogilvie and other Metra stations.
The bikes on the racks around the perimeter usually look pretty picked-at/vandalized to me though.
I would not worry much about a "non-descript" bike that's locked with a decent U-lock though- the angle grinder folks are after nicer stuff as a rule.
Just be sure you lock to a city bike rack; some friends locked to a metal fence near Union Station about 2-3 years ago and a health club decided it had the right to cut the U-locks and throw the bikes in a storage room. They only tracked down their bikes by dumb luck.