Simmer all ingredients, except chicken, until thickened, about 30 minutes.
Preheat a grill to medium-high (you may also use oven broiler).
Season bone-in, skin-on chicken breast halves with salt and pepper.
Grill over direct heat until golden and crisp on both sides, about 5 minutes.
Transfer to a bowl and toss with 1 cup of the sauce.
Place on the cooler side of the grill.
Mix sauce ingredients in a bowl.
Turn broiler off and oven to 400F - cover and cook, basting once, until the meat is glazed and reaches 165F or the juice is clear.