1. Rinse chicken and pat dry. In a 1-gallon heavy plastic food bag, combine chicken, apple juice, garlic, and pepper. Seal bag, set in a bowl, and chill at least 4 hours or up to 1 day; turn over occasionally.
2. Prepare barbecue. If using charcoal briquets, mound and ignite 60 briquets on the firegate of a barbecue with a lid. When briquets are dotted with gray ash, in the 15 to 20 minutes, push equal amounts to opposite sides of firegrate. Add 5 more briquets now, and every 30 minutes of cooking, to each mound of coals.
If using a gas barbecue, turn heat to high and close lid for 10 minutes. Adjust burners for indirect cooking (no heat down center) and keep on high. Set a drip pan on firegrate between coals or burners.
Set barbecue grill in place.
3. Lift chicken from marinade and lay on grill, not over heat. Cover barbecue; open vents for charcoal. Baste with marinade occasionally during the first 20 minutes. Cook chicken until no longer pink at bone of thickest part (cut to test), 40 to 45 minutes. Discard marinade. Brush all sides of chicken with honey. Cook until browned, turning as needed, 3 to 4 minutes longer. Transfer to a platter. Add salt to taste.