We had grilled chicken like this in Portugal, and yesterday Dad and Russell recreated it.
1 medium broiling chicken (3 to 4 pounds), split in half through the breastbone
Red chile flakes
Several cloves of garlic
Juice of one lemon
1 rubber mallet
Pound the chicken with salt, chile flakes, and garlic to flatten slightly, in order to make each half more or less an even thickness. Squeeze the lemon juice over all and let sit for an hour or so.
Grill indirectly over a hot charcoal and mesquite fire (that is, put a drip pan in the middle and push the hot coals to the side before putting on the chicken) and grill, covered, for one hour, turning every 15 minutes. Let rest ten minutes or more before serving.