Combine oil, lemon juice, vinegar, lemon peel, basil, garlic, salt and pepper in a shallow baking dish. Add chicken, turning once to coat both sides. Refrigerate for 30-45 minutes, turning once. Prepare charcoal or heat broiler. Grill or broil chicken 4 inches from heat, turning once, 3-5 minutes per side, or until completely cooked through. This can be very low in cholesterol depending on what oil you use.