For the brine, in a mixing bowl combine the water, salt, sugar, garlic, and thyme. Transfer the brine to a 2-gallon sized re-sealable plastic bag. Add the chicken, close the bag and refrigerate 2 hours (if you've only got 15 minutes, that's fine) to allow the salt and seasonings to penetrate the chicken.
Meanwhile, make the sauce. Wrap the bacon around the bunch of thyme and tie with kitchen twine so you have a nice bundle. Heat about 2 tablespoons of oil in a large saucepan over medium heat. Add the thyme and cook slowly 3 to 4 minutes to render the bacon fat and give the sauce a nice smoky taste. Add the onion and garlic and cook slowly without coloring for 5 minutes. Add the remaining ingredients, give the sauce a stir, and turn the heat down to low. Cook slowly for 20 minutes to meld the flavors. Once the sauce is done cooking, remove about 1 1/2 cups of the sauce and reserve for serving along side the chicken at the table. The rest of the barbecue sauce will be used for basing the legs.
Preheat oven 375 degrees F.
Preheat a grill pan or 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. Take the chicken out of the brine, pat it dry on paper towels. Arrange the chicken pieces on the preheated grill and cook, turn once mid-way, and cook for a total of 10 minutes. Transfer the grill marked chicken to a cookie sheet and then place in the oven. Cook the chicken for 15 minutes, remove it from the oven and then brush liberally, coating every inch of the legs with the barbecue sauce and then return to the oven for 25 to 30 more minutes, basting the chicken for a second time half way through remaining cooking time. Serve with extra sauce.
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