Brine the chicken as follows: Combine water, salt, sugar, garlic, and thyme in a 2-gallon sized resealable plastic bag.
Add the chicken, close the bag and refrigerate 2 hours (if you've got only 15 minutes, that's fine) to allow the salt and seasonings to penetrate the chicken.
Meanwhile, make the sauce as follows: Wrap the bacon around the bunch of thyme and tie with kitchen twine so you have a nice bundle.
Heat the 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 smoky taste.
Add the onion and garlic. 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.
Cook the chicken as follows: Preheat an outdoor gast or charcoal barbecue to 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 non-stick surface.
Remove the chicken from the brine, pat the chicken dry on the paper towels.
Arrange the chicken pieces on the preheated grill and cook,turn once mid way, and cook for a total of 15 minutes.