Heat oil in a large Dutch oven over medium heat. Add onion, rosemary, and garlic; sauté 2 minutes. Add zucchini, black pepper, salt, and chicken; cook 5 minutes until chicken is browned, stirring to crumble.
Add broth and next 6 ingredients (through bay leaf); bring to a boil. Reduce heat, and simmer 30 minutes. Discard bay leaf. Sprinkle with cheese.