I certainly don't see anything above to disagree with, but thought adding a point or two might be helpful. There are available sauce and rub recipe sources galore, but if you only had time to look at two, Paul Kirk's Championship Barbeque Sauces
and Steven Raichlen's Sauces, Rubs and Marinades
would be decent choices. With those books in hand, thinking analytically about the sauce you had in Chicago may begin to hint at tastes of certain ingredients and replication attempts can be made. It may take a few tries, and you may never copy the original exactly, but the bet is you'll end up with a really good sauce each time you try.
Secondly, if you've never tried brining your chicken before grilling, it's a step that can help take your meal from a "6" to a "10" simply by maintaining a high moisture level for the meat. Again, a legion of recipes are floating around, but a very simple (yet quite tasty) brine can be made by adding a 1/2 cup of each kosher salt and brown sugar (I prefer dark brown), a rough chopped onion, a half dozen or so garlic cloves, and a tablespoon or so of cumin seeds to two quarts of water. Bring to a hard boil, and then begin the process of getting the temp down to cool (I generally let it sit out for a couple hours, then refrigerate long enough for it to be cool). Soak the chicken anywhere from 4 hour to overnight in the brine, then remove and soak in clean water for a bit (say an hour if you brined all night long) to draw out some of the salt for taste purposes.
I generally grill chicken indirectly, and using that method, once the meat's juices are clear, the bird is done...and given these steps, incredibly moist. The process should protect the meat even if you want to leave it on the grill longer to achieve a darker color.