Make the chicken: Preheat a grill to medium high and oil the grates. Combine the brown sugar, chili powder, smoked paprika, mustard powder, garlic powder and cayenne in a small bowl.
Place the chicken between 2 sheets of plastic wrap and pound with a heavy skillet or the flat side of a meat mallet until an even 1/2-inch thickness. Rub the chicken with the sugar mixture; set aside while you make the onion-bacon jam.
Make the onion-bacon jam: Heat the olive oil in a medium dutch oven over medium heat. Add the bacon and cook until crisp, 5 to 7 minutes. Remove to paper towels. Pour out all but about 2 tablespoons fat, then add the onions and cook over low heat, stirring, until caramelized, 20 to 25 minutes. Stir in the thyme and bourbon; simmer 1 minute. Season with salt and black pepper. Stir in the bacon, brown sugar, cider vinegar, Worcestershire sauce and 1/4 cup water; simmer 2 more minutes.
Season the chicken with salt and black pepper and grill until browned and well marked, 2 to 3 minutes. Flip and grill until the chicken is cooked through, about 2 more minutes.