Skillet Chicken, Zucchini, and Cheesy Rice

Name: Skillet Chicken, Zucchini, and Cheesy Rice
Yield: Serves 4
Ingredients: 1 cup, long-grain white rice; 4 tablespoons, unsalted butter; 2 , zucchini, shredded; 1 , onion, chopped fine; 2 teaspoons, chopped fresh thyme; 1/2 teaspoon, table salt; 1/2 teaspoon, pepper; 1 (2½-pound), rotisserie chicken, skin and bones discarded, meat shredded into bite-size pieces (3 cups); 1 cup, chicken broth; 4 ounces, sharp cheddar cheese, shredded (1 cup); 1 1/2 ounces, Parmesan cheese, grated (3⁄4 cup); Chopped, fresh basil for serving