Smokedaddy at 1804 W. Division is one of my favorite places in Chicago for BBQ meats of any sort (ribs, pulled pork, brisket. Their ribs are huge.)
If you want something a little different, and slightly further down the street, there's Papa's on about 2500-ish W. Division (on the south side of the street, about 3 streets past Western.) They're more a hole-in-the-wall, and they don't serve beer, but they have fantastic Puerto Rican rotisserie chicken and -one of my favorite sandwiches in the city: the jabarito. If you've never had this local culinary invention, do give it a shot one day. It's basically a garlicky cheesesteak sandwich served on deep fried plantains instead of bread. It is simply fantastic.