Combine chicken broth, rice, and 1/2 cup water in a saucepan over medium-high heat. Bring to a boil; reduce heat and simmer until rice is almost tender, about 15 minutes.
Heat olive oil in a large skillet over medium-high heat. Cook mushrooms, green bell pepper, onion, and celery until tender, about 7 minutes. Stir in cooked rice, chicken breasts, 1 cup water, parsley, oregano, salt, and black pepper. Simmer until chicken is no longer pink in the center, 20 to 25 minutes. Top with Parmesan cheese.
