Rub chicken and cavities with 2 tablespoons olive oil, garlic cloves, salt, and pepper.
Tuck chicken wings under; tie legs together with string, if desired. Pour remaining 1 tablespoon oil into a large cast-iron skillet; place chicken, breast side up, in skillet.
Place 1 rosemary sprig and 2 lemon quarters into neck cavity of chicken; repeat in lower cavity. Place remaining rosemary sprig underneath skin.
Bake at 450° for 30 minutes; reduce heat to 350°, and bake 1 hour. Serve with Jan's Roasted Potatoes.