In 6-quart dutch oven, melt butter on medium-high. Add onion, celery, and green pepper, and cook 6 minutes or until softened, stirring. Add chicken, garlic, and seasonings; cook 2 minutes. Stir in tomato paste, then sausage; cook 2 minutes longer.
Add tomatoes with their juice, broth, rice, and ham; heat to boiling on high. Reduce heat to low; cover and simmer 20-30 minutes or until liquid is absorbed.
Discard bay leaves; garnish with green onions if you like.