Add first 8 ingredients to a large saucepan, blending well. Bring to a boil over medium high heat, reduce heat to low and simmer about 15 minutes, or until reduced to about 1 1/2 cups.
Meanwhile, heat your outdoor grill on low heat. Place chicken breast on grates of grill, bone-side facing down and to the side of the heat source so chicken does not actually touch the flames. Close lid and cook for 15 minutes, keeping an eye out for flame-ups and charring. Turn chicken so skin side is facing down and continue cooking another 15 minutes. This time keep a more careful eye out for flames and charring, since the skin is fatty. (The chicken will not be completely cooked at this stage, which is what we are after.)
Start brushing sauce over the chicken and continue to cook without closing lid, moving breasts over the flames at this point. Turn the chicken breasts as often as needed to prevent burning chicken, slathering on the sauce every time you turn.
Cook until chicken is completely cooked. Remove to serve hot.