Heat oil in a large heavy saucepan or Dutch oven over medium-high heat. Add sausage, celery, onion, bell pepper, and garlic. Cook 5 minutes or until vegetables are tender, stirring frequently.
Stir in broth, tomatoes, bay leaf, TABASCO® Sauce, oregano, thyme, and allspice. Bring to a boil, reduce heat, and simmer uncovered for 10 minutes, stirring occasionally. Stir in rice; cover and simmer 15 minutes. Add shrimp; cover and simmer 5 minutes longer or until rice is tender and shrimp turn pink. Let stand, covered, 10 minutes. Remove bay leaf before serving.
Makes 4 servings.