In a large mixing bowl, combine the water, salt, sugar, garlic and thyme. Transfer the brine to a 2 gallon ziplock bag or large bowl and add chicken. Place in fridge for 2 hours.
While chicken is marinating, make the BBQ rub. Just mix all of the ingredients in a small bowl and set aside.
Spread charcoal through half of the grill and preheat grill to medium-high heat, about 400°F. Wipe grate with oil to make sure chicken doesn't stick when you cook it. Take chicken out of brine and pat down with paper towel. Sprinkle the BBQ rub over both sides of the chicken.
Cook the chicken the chicken skin-side down on direct heat for 5-10 minutes or until you get grill marks. Flip and cook for another 5 minutes. Remove the chicken to indirect heat. Brush BBQ sauce throughout chicken. Cover and cook for another 20-30 minutes or until it reaches 165°F, basting the chicken with BBQ sauce every 10 minutes.
Do not skip soaking the chicken in the brine for 2 hours. This gives additional flavor and keeps the chicken juicy.
Pat the chicken dry after soaking in the brine which allows the skin to get crispy when grilling.
Spread charcoal over half the grill so you can have direct and indirect heat, which means you won't overcook the chicken.
Brush the BBQ chicken kebabs with the barbecue sauce when grilling. Make sure you rotate the skewers every 5 minutes or so. You want to get a char but not completely burn everything.
You know the chicken is cooked when it reaches 165°F with an instant-read thermometer or if you cut into the chicken and the juices run clear and there is no pink. Honestly, I always just cut the chicken to see when it is done. If it isn’t just cook slightly longer.
Leftovers will store well in the fridge for 2-3 days in an air-tight container or be frozen for 3 months.