When flames have all died down and coals are covered in white ash, place chickens, breast sides down, on side of grill away from coals, legs facing away from coals (be careful that none of meat is directly over coals). Put lid on grill with vents open one quarter of the way.
Roast 30 minutes, then turn chickens over and add another 1/2 shoebox (about 30 briquettes) of new charcoal. Continue roasting 45 to 50 minutes more. To check for doneness, cut into thickest part of a thigh, all the way to bone; there should be no sign of pink. (It’s not easy to take the temperature of a flattened bird, but if you do use a thermometer, look for a final temperature of 170°F in fleshy part of thighs; do not touch bone.) Transfer chickens to a carving board and loosely cover with foil.