In 12-inch nonstick skillet, heat oil over medium-high heat. Cook chicken and garlic in oil 4 to 6 minutes, stirring frequently, until chicken is brown.
Stir in broth and pasta. Heat to boiling; reduce heat to medium. Cover and cook 10 to 15 minutes, stirring occasionally, until pasta is tender and most of liquid is absorbed.
Stir in tomatoes and zucchini. Cook uncovered 5 to 10 minutes, stirring occasionally and breaking up tomatoes with spoon, until zucchini is tender. Sprinkle with cheese.