Preheat grill to medium. Combine garlic, 1/2 teaspoon salt and 1/4 teaspoon pepper in a small dish; mash into a paste using back side of a large spoon. Add lime peel.
Wash hands. Loosen skin of chicken by slipping your hand between the meat and skin. Spread a quarter of the garlic mixture and tuck 2 cilantro sprigs under the skin of each breast. Wash hands.
Combine chopped cilantro, butter or margarine, oil and lime juice in a small bowl. Brush chicken skin lightly with mixture. Sprinkle with remaining 1/2 teaspoon salt and 1/4 teaspoon pepper.
Place chicken on grill, skin side down. Brush with cilantro-butter mixture. Cover and grill 15 minutes. Turn chicken; brush with half of remaining cilantro butter. Cover and grill 10 minutes. Without turning, brush chicken with remaining cilantro butter. Cover and grill 5 minutes or until done (internal temperature 180° F).
Serving suggestion: Serve with Spanish Rice and Chilled Fresh Fruit. Refrigerate leftovers.