Cook pasta according to package directions, omitting salt and fat. Set aside.
While pasta cooks, combine chicken, broth, and water in a large Dutch oven. Cover and bring to a boil. Reduce heat, and simmer 3 minutes or until chicken is cooked.
Remove chicken with a slotted spoon; keep warm. Stir in tomatoes; cook 1 minute or until thoroughly heated. Stir in spinach; cook 2 minutes or until spinach wilts.
Add cooked chicken and pasta to pan; cook 1 minute or until thoroughly heated. Stir in pesto and pepper. Ladle soup evenly into 6 bowls, and sprinkle with Parmesan cheese, if desired.