This sweet, tangy BBQ chicken recipe is a simple way to make slow-cooked, delicious, barbecue chicken on the grill. To cook using indirect heat you'll want to have high heat on one side of the grill and very little to no direct heat on the other side of the grill, where the chicken resides for most of the cooking time. During the saucing portion of cooking it's ok if the chicken flames up as you're turning it over. This is why you're using long-handled tongs. Cooking the chicken in a little fire here is ok, but don't let them sit in the fire for more than 15 to 20 seconds at a time.