In a shallow dish, mix together oil, lemon juice, marjoram and thyme.
Prick chicken flesh with a fork. Turn chicken to coat with the marinade. Cover dish and marinade in refrigerator up to 8 hours.
Preheat broiler. Remove chicken from marinade and place, skin side down, on broiler pan. Brush with marinade and broil 8-10 minutes, basting occasionally. Turn chicken and broil an additional 8-10 minutes. or until golden-brown and cooked through.
Stir pan juices into the cooked warm rice, garnish with thyme, marjoram and lemon peel.