In a non-metallic medium sized container combine lime juice, oil, honey, thyme, rosemary and garlic. Whisk together until well blended.
Marinate chicken breasts in lime mixture for 1 to 2 hours. Place on a lightly greased broiling pan. Cook under broiler 3-4 inches (10 cm) from element. Baste once or twice in the first half of cooking time until chicken is cooked through. Makes 4 servings.