In a large skillet over medium heat, brown chicken in 2 tablespoons oil. Remove chicken and set aside. Add remaining oil to skillet. Saute onions and garlic until tender. Add parsley, tarragon, salt and pepper; mix well.
Return chicken to skillet; cover with onion mixture. Sprinkle with olives. Reduce heat; cover and simmer 40-45 minutes or until chicken is tender and juices run clear. Serve over rice or noodles.