Cook rice in drippings in a small cast-iron skillet, stirring frequently, until rice is lightly browned. Set aside.
Sauté onion, green pepper, green onions, parsley, and ham in oil in a Dutch oven until vegetables are tender. Stir in browned rice. Add broth, tomatoes, bay leaf, garlic, thyme, pepper, and hot sauce; stir until blended. Cover and cook over low heat 1 hour or until liquid is absorbed. Stir in chicken.