Mix brine ingredients with 2 qts. water in a 2-gal. resealable plastic bag. Add chicken, seal, and chill for 15 minutes to 2 hours.
Make sauce: Wrap bacon around thyme; tie with kitchen twine. Heat oil in a saucepan over medium heat. Add thyme bundle and cook 3 to 4 minutes. Add onion and garlic. Cook over medium-low heat, stirring until softened, about 5 minutes. Stir in remaining ingredients and cook over low heat, covered, 20 minutes. Remove thyme; spoon 1/2 of sauce into a bowl.
Prepare a gas barbecue for two-level heat (500° to 550° in one area and about 300° in another). Wipe cooking grate with oiled paper towels. Pat chicken dry with more paper towels, sprinkle with salt and pepper, and drizzle with some oil.
Grill chicken skin side down on high-heat area 5 to 7 minutes. Move pieces to cooler area, turning over, and cook 20 minutes, covered. Spoon sauce from pan onto skin side and cook chicken until an instant-read thermometer measures 160° at thickest part (or cut to test), 15 to 20 minutes. Let rest 5 minutes. Serve with sauce in bowl.
Add moisture. Brine your chicken using a solution of salt, sugar, and seasonings. The meat will plump up and absorb the seasonings, so the flavor isn't just on the skin. (This also works really well for pork and short ribs.)
Set up two heat zones. Create a hot zone and a medium to low zone. One mistake people make is grilling thicker cuts, like bone-in chicken and pork chops, over direct high heat. They'll burn on the outside and stay raw inside.
Start the chicken skin side down. To get crispy, golden skin, put it skin side down over the hot zone and let it turn a nice, golden brown. Then flip it over onto the medium zone to finish cooking.
Make your own barbecue sauce. It's easy and you'll look like a rock star.
Note: Nutritional analysis is per piece.