1.In a bowl, stir together the garlic, salt, lemon zest, and rosemary. Rub the chicken all over with the garlic mixture, including under the skin. Set aside for 30 minutes at room temperature.
2.Preheat the broiler to high. Arrange one oven rack in the lower-middle of the oven and a second rack in the upper-middle, about 4 to 6 inches from the heating element. Place the chicken on the rack of a sheet pan. Turn the chicken skin-side down on the rack.
3.Broil the chicken on the lower-middle rack until it starts to brown, about 15 minutes. Turn the breasts skin-side up and broil until the skin starts to crisp, about 10 minutes longer.
4.Move the pan to the upper rack, brush the skin with the lemon juice and olive oil, and continue to broil until the skin is crispy and browned, about 3 minutes longer. Serve.