Allow me to also nominate Chicago French Market. I've been there many times and my favorites are Lillie's, a bbq joint with great pulled pork and mac and cheese, and Saigon Sisters, which serves Vietnamese dishes. If you want a little sweet to finish things off, there is a bakery called Vanille. All their offerings look amazing; I've only tried the brownie myself, which is so rich you could probably split one between two people and still be sated. I'm fairly sure there is a place within the Market to buy fresh produce as well.
Depending on the day you arrive in Chicago, you might be able to get straight-from-the-farm fresh produce at one of the city's Farmers' Markets in the Loop. On Tuesdays, there's a Market at Federal Plaza, on the southwest corner of Adams and Dearborn, about .5 mile due east of Union Station. On Thursdays, there's a Market at Daley Plaza, on the northeast corner of Clark and Washington, which is about .7 mile east and north of Union Station.
If basic, no-frills produce is OK with you, there is a small WalMart in the Presidential Towers complex, northeast corner of Monroe and Jefferson, just a couple of blocks from the station.
Hope that helps.
Edit - Just looked at the Chicago French Market website, and you can get produce there, at a place called City Fresh Market. Also, there is also a Farmers' Market on Thursdays at Sears Tower (Willis Tower, whatever), which is just over the river. Not sure where on the property it's held, but the only open plaza space is on the south end of the building, along Jackson.