Saute chicken and sausage in a large skillet for 4 to 5 minutes. Remove meat from skillet, add green onions and onion and saute until soft. Set aside.
To Make Roux: In a small saucepan stir together oil and flour over low heat; cook until color is caramel and mixture is reduced to 1 cup of roux. Set aside.
Put water in a large pot. Add the chicken, sausage, onion mixture, celery, seasoning, cayenne pepper, salt, ground black pepper and garlic. Bring all to a boil and cook for 20 minutes. Add 1/2 cup roux and stir together; the mixture should have the consistency of chowder. If necessary, add the remaining 1/2 cup roux.
Reduce heat to medium low and simmer uncovered for 2 hours, stirring occasionally. Serve hot over rice, if desired.