The chicken comes off right after the sauce goes on.
In my experience—not as a barbecue champ or a cooking instructor but as a dinner guest—the food I see most abused when I go to a cookout is chicken. The combination of fatty skin, sweet barbecue sauce, and high heat results in what often looks like chunks of cinder. You can try scraping off that bitter, black coating, but its flavor and aroma—what I call "eau d'ashtray"—flavors the meat.
The secret to great barbecued chicken, one with moist, tender meat and sticky, pleasantly smoky skin, is to lower the heat of the fire and leave the sauce off until the last minutes of cooking. Most of the flavor comes from a spice rub that's been on the bird from the get-go and from the smoke of the fire, both of which fully permeate the meat during the long, slow cooking.
My method may take longer than most recipes for barbecued chicken, but there's less work involved. Because you're cooking over a low fire, and because the sauce (the real culprit behind cinder-chicken) doesn't go on until late in the game, you don't have to stand vigil, moving chicken pieces around a hot fire and trying in vain to stave off the inevitable flare-ups.