Combine garlic and oil in a bowl.
Cut up either side of back bone from tail to neck. Remove backbones. Open chickens up flat like a book, breast side down. Tuck wing tips underneath. Cut slit on either side of breast tip. Insert tip of each drumstick into a slit. Cover chickens with plastic wrap. With flat side of meat mallet, pound thicker parts of drumsticks and shoulder sides of breasts for even thickness.
Season with salt and pepper. Rub garlic oil over chickens. Place on baking sheet. Cover; refrigerate at least 30 minutes.
Lightly brush grill rack with vegetable oil. Then prepare grill with low-heat coals or heat gas grill.
Place chickens, breast side down, on grill rack. Grill, covered, until lightly browned, 10 to 12 minutes. Turn over; grill, covered, 10 minutes, basting with any garlic oil remaining on baking sheet. Turn over again. Grill, covered, 10 minutes.
Turn over. Grill, uncovered, 10 to 15 minutes, until temperature registers 175°F in thickest part of thigh. Cut into serving pieces.
Heat oven to 375°F. Coat broiler-pan rack with nonstick cooking spray. Place chickens, breast side down, on broiler-pan rack. Bake 16 minutes. Turn over; bake 15 minutes. Turn over; bake 20 minutes. Turn over; bake 10 minutes, until temperature registers 175°F in thickest part of thigh.