The Aldi in Englewood isn't really a supermarket - it's more like a dollar-store version of Trader Joe's. They also don't sell much produce (maybe 10 feet of shelf space), and it's usually been sitting on the shelf a while. I think this is more about customer demand than availability. Chicago gets plenty of great produce through its wholesalers (and role as a freight hub) - high quality produce is abundant and cheap at the Latino markets.
Fair enough! The one over here has a pretty solid frozen vegetable section and reasonably good fresh produce ($0.99 unripe avocados!!!). I'd estimate that they have about 20ft of shelf space for fresh stuff.
This by the way is what Aldi's are like in their home country, Germany. When we stayed with my mother in law it was pretty much the only grocery store around (and in an agricultural area!).