Around me, I see woefully little, even at the independent markets I shop at.  I rarely, if ever, shop at Jewel or Dominick's. 

Tony's on Elston is probably the closest store I use that could be considered a supermarket. Their produce section is hit or miss, and most of it comes from Mexico.

Family Fruit Market on Cicero and Lincolnwood Produce are both the same. Neither intentionally stocks or advertises local produce. I feel like if it does show up, it's an accident.  It's all California or Mexico or S. America.

Eggs, cheese, and prepared meats are a different story at these places. There's plenty of inexpensive, bulk Wisconsin cheeses at these places, Phil's fresh eggs, and Bobak's sausages (and Tony's makes their own Mexican chorizo and Italian sausage).

Best,
Michael