Cut chicken breasts in half crosswise to get a total of 10 pieces of chicken. Season with Creole seasoning. Measure flour into a large paper bag. Add chicken pieces and shake until well-coated. Remove chicken and reserve the flour.
In a large skillet, brown chicken in very hot oil, remove and set aside. Stir oil remaining in the skillet with a wire whisk to loosen any brown particles remaining in the bottom of the pan. Make a roux by whiskingÂ in 1 cup of the remaining flour and stiring constantly until the roux turns a dark brown. Remove from heat; add onions, celery and green bell pepper, stirring constantly until vegetables are tender.
Transfer roux and vegetables to a Dutch oven. Add stock to roux and vegetables and bring to a boil. Reduce heat to simmer and add garlic, sausage and chicken. Continue cooking, covered, until the chicken is tender, 1 3/4 to 2 hours.
Adjust seasonings and serve in bowls over the rice.