Prepare Broiled Chicken or Grilled Chicken. Rub the pieces lightly with vegetable oil before broiling or grilling and omit the salt and pepper. Prepare Teriyaki Marinade and simmer, stirring, in a small saucepan over medium heat until slightly thickened. About 2 minutes before the chicken is fully cooked, brush both sides with about ¾ cup of the sauce. Return to the broiler skin side up or to the grill skin side down and cook until the skin is lightly charred. Serve with additional sauce.