There is a parking garage located just south of Union station which has an underground connection to the station. It cost 22 dollars a day to park there. You can use a credit card to pay. You can enter from Canal or Clinton.
I have parked there numerous times without a problem. However, on one occasion, my car was broken into and my aftermarket Ipod car radio was stolen as well as a GPS. The dashboard was damaged too. I know I left things in sight because I was traveling with others, and was distracted. I suspect I also left the car unlocked. Two things that would make the car an easy target, The garage people, needless to say were not concerned.
So if you park there, put valuables in the trunk, and make sure you lock it. You will probably be ok.
Chicago traffic is very unpredictable. Allow plenty of time. I would advise trying to arrive by noon or earlier. If traffic is really backed up on the Dan Ryan, you can get off at 22nd street or Canalport and make your way to the station on surface streets. If you are interested in doing this, check out a map before you go.