Preheat an outdoor gas or charcoal barbecue to a medium heat. Take a few paper towels and fold them several times to make a thick square. Blot a small amount of oil on the paper towel and carefully and quickly wipe the hot grates of the grill to make a nonstick surface. Arrange the chicken breast on the preheated grill and cook, turn once mid-way, and cook for a total of 8 minutes.
Transfer the grill marked chicken to a cookie sheet and then place in the oven. Cook the chicken for 10 minutes, remove it from the oven and then brush liberally, coating every inch with the barbecue sauce and then return to the oven for 10 to 15 more minutes, basting the chicken for a second time half way through remaining cooking time. Serve with extra sauce.
To make the Barbecue sauce, heat oil in a saucepan and sauté garlic until light brown. Add other ingredients and heat until it bubbles, turn down heat and simmer for 1 hour. This reduces the sauce a bit and gives it a dense thickness.