Heat oil in a large skillet over medium-high heat. Sprinkle chicken with salt and black pepper. Add chicken to pan, and cook 5 minutes or until lightly browned, stirring occasionally. Remove chicken from pan; cover and keep warm. Add sausage to pan; cook 5 minutes or until lightly browned, stirring occasionally. Add 1 cup onion, bell pepper, celery, and garlic; cover, reduce heat to low, and cook 12 minutes or until vegetables are tender, stirring occasionally.
Stir in rice; cook 2 minutes, stirring constantly. Add broth, paprika, thyme, and red pepper; bring to a boil. Cover, reduce heat, and simmer 15 minutes. Add chicken and tomatoes; cook, uncovered, 10 minutes or until liquid is absorbed. Stir in shrimp; cover and cook 5 minutes or until shrimp are done. Remove from heat, and let stand 5 minutes. Fluff with a fork. Sprinkle with green onions.