Open Produce is an extremely vegan-friendly produce market in Hyde Park. There is an excellent selection of vegan prepared foods (boxed lunches from Soul Vegetarian and other local restaurants), desserts (vegan brownies and individually-wrapped Tofutti Cuties), as well as "staples" like Daiya cheese and Earth Balance margarine. Best of all, Open Produce is open until 2 AM every night, making it "the latest place to buy fresh produce in Hyde Park."
Open Produce is run by two recent computer science graduates of the University of Chicago (one of whom is vegan), who keep up-to-date information about their products and graphs of their sales trends on their website. They're also very receptive to suggestions of vegan products that they could stock.