In 5-quart Dutch oven or saucepot, heat 2 tablespoons oil over medium-high heat. Add chicken and brown on all sides, about 10 minutes. Remove chicken from pot.
Add remaining 2 tablespoons oil to pot and heat. Add pork, sausage, celery, onion, green pepper and garlic; cook 8 to 10 minutes or until tender, stirring frequently. Stir in tomatoes, broth, tomato paste, TABASCO® Sauce, bay leaf, salt, oregano, thyme and allspice.
Return chicken to pot. Cover; reduce heat and simmer 10 minutes. Stir in rice. Cover. Simmer 40 minutes or until chicken and rice are tender, stirring frequently and adding additional broth if rice begins to stick to bottom of pot.
Makes 8 servings.