Step 1With a mortar and pestle or in a blender, grind the garlic, rosemary, salt and fennel seed. Continue grinding while adding the olive oil to make a coarse paste.
Step 2Using a pair of poultry shears or a chef's knife, cut the chicken alongside the backbone, all the way from neck to stern. Repeat on the other side of the backbone, removing it from the carcass.
Step 3Place the chicken skin-side up on the cutting board, opened out like a book. Firmly press down on the center of the breast to crack the sternum and flatten the chicken. Place the chicken in a resealable plastic bag and spoon in the herb mixture. Press out all the air, seal tightly and massage to distribute the marinade evenly. Refrigerate overnight or leave at room temperature for 1 hour.
Step 4Wrap a 1-foot-square paving stone in aluminum foil. Start the coals in a chimney and when they are lightly coated with gray ash, about 20 minutes, empty them into the grill, arranging them in a gentle slope against one side. Replace the grill rack and brush it with oil.
Step 5Place the chicken skin-side down on the grill rack, away from the direct heat but with the drumsticks pointing toward the fire. Brush one side of the foil-covered brick with oil and place the brick on top of the chicken.
Step 6Grill until the skin is well-browned, about 20 minutes. Remove the brick and turn the chicken over, placing it skin-side up directly over the fire. Cook until the juices at the hip and knee joints run clear when pierced with a knife, about 5 minutes. Remove to a carving board and let rest 5 minutes to distribute the juices evenly before carving. Serve immediately.