Heat oil in a large Dutch oven over medium-high heat. Add sausage; cook until sizzling quiets (about 8 minutes), stirring occasionally.
Add bell pepper, onion, celery, and bay leaves; cook until vegetables are golden brown, sizzle loudly, and begin to squeak (about 14 minutes), stirring occasionally. Add chicken and next 8 ingredients (through garlic); cook 4 minutes, stirring occasionally.
Add tomato puree; cook 2 minutes, stirring occasionally. Add broth, and bring to a boil. Stir in rice. Cover, reduce heat, and simmer 20 minutes. Discard bay leaves. Stir in green onions.