In a large Dutch oven, heat olive oil over medium-high heat. Add chicken, and cook for 10 minutes, stirring frequently. Add onion and carrot, and cook for 5 minutes. Stir in zucchini, diced tomatoes, and chicken broth. Bring to a boil; reduce heat, and simmer, uncovered, for 30 minutes. Top each serving with grated Parmesan, if desired.