Heat oil in a 5-quart saucepan over medium heat; add celery, green pepper, and onion and cook 5 minutes. Add potatoes and cook 5 minutes longer, stirring occasionally.
Stir in flour and cook 1 minute. Add chicken broth, TABASCO® Sauce, thyme, allspice and salt and bring to a boil, stirring often. Reduce heat to low, cover, and simmer 10 minutes.
Add chicken; cover and simmer 5 minutes longer or until chicken and potatoes are tender. Stir in chopped parsley and serve.
Makes 6 servings.