The only Greek market in Chicago that I'm aware of is
Ellinikon Pandopoleion on the East Side. It's a quaint shop, worth a visit, but I doubt it will take care of all your Greek needs.
In the city, you can find some Greek products at multi-ethnic grocers such as Devon Market (1440 W Devon) and A&G Market (5630 W Belmont). Don't forget Treasure Island is Greek owned so they have some Greek foods (eg, cheeses, Easter specialties) you might not expect.
Fairly close to Chicago is Brillakis Import Foods in Niles, a pretty good all-Greek grocery. But the best Greek market by far is
Minos Imports in Addison, quite a hike from the city.
Ellinikon Pandopoleion
10538 S Ewing Av
Chicago
773-734-2683 (?)
Brillakis Import Foods
9061 N Courtland Dr
Niles IL
847-966-1250
Minos Imports
648 W Lake St
Addison IL
630-543-0337