Umm, where's it at Chitown? I lived there until 1992 and never heard of this place.
We always went up to the Plush Horse off of Southwest Hwy and about 123rd or so in Palos. Until they stopped making their own and bought commercial. Then we had nowhere for homemade.
Speaking of Ice Cream. I worked in, at the time, the world's largest novelty ice cream factory back in the 90s. You can not believe how great unfrozen ice cream right out of the freezer. And we were encouraged to taste the ice cream constantly to make certain it was good.
Next time you go in to Margies - ask if they are currently making ice cream. If they are, whatever flavor, ask if you can have a cup of it before it goes into the blast freezer, right out of the ice cream freezer.
If that sounds confusing the ice cream freezer is a scraped surface heat exchanger, that forms the crystals and injects the air for over-run. It comes out paste like at this point, so it can be used to fill cups, 1/2 gallons, bigger containers, or used to make novelties (things on a stick or cones, like Drumsticks). This is before it gets blast frozen. It is by far much better than the hard ice cream. Even if served at the right temperature after blast freezing, it is not as good as right out of the freezer.