In a large Dutch oven or soup pot, heat the olive oil over medium-high heat. Add the carrots, onions, celery, and garlic. Sauté for 5 minutes or until the vegetables are softened.
Cook the soup:
Add the seasonings, broth, and water to the pot. Bring the soup to a boil, reduce the heat, and simmer for 15 minutes.
Stir in the spaghetti and shredded chicken. Cook for 10 minutes or until the pasta is tender.