Melt butter in large saucepan over medium heat. Add onion; sauté until translucent, 5 to 7 minutes. Add ketchup, molasses, mustard, brown sugar, Worcestershire, pepper and chili powder.
Reduce heat to medium-low and simmer until sauce thickens and coats the back of a spoon (12 to 15 minutes). Take the sauce off the burner and carefully add the bourbon; stir to incorporate the bourbon then return to the burner. Cook until heated through, about 3 minutes. Season with salt and pepper to taste. (Can be made 1 day ahead. Cover and chill.)
Season chicken legs with salt and pepper.
Prepare kettle barbecue for indirect cooking, by placing briquettes in the center and placing chicken parts around the outside.
Grill the chicken parts until juices run clear and skin is golden, turning to cook all sides, about 1 hour. Brush chicken with sauce and cook until glaze forms, about 15 minutes longer (turning chicken several times to keep sauce from burning). Serve.