Pork shoulder is one of the cornerstones of American barbecue--right up there with brisket and ribs. It's certainly the most flexible: you can smoke it. Indirect grill it. Spit-roast it on a rotisserie. It's also the most forgiving: it stays moist even when you overcook it.
When it comes to barbecue, Chicago isn't usually the first city to come to mind. "Chicago Style" barbecue is a questionable mix of techniques often involving a combination of dry rub, sauce, and usually some slow roasting or even boiling of ribs.