Heat oil in a cast iron skillet over medium heat; stir in onion. Cook and stir until the onion is softened and lightly browned, about 8 minutes. Lower heat and add bell pepper, mushrooms, and garlic; cook and stir until soft, 3 to 5 minutes more.
Mix oregano, basil, paprika, black pepper, and salt together in a bowl. Stir 1/2 of the herb mixture into vegetable mixture. Stir black beans and rice into vegetable mixture. Arrange chicken breasts over beans and rice mixture, sprinkle remaining herb mixture on top. Pour in tomatoes and 1 cup water. Cover skillet with aluminum foil.
Bake until chicken is no longer pink in the center and the juices run clear, adding more water as needed to keep mixture moist, about 25 minutes. Remove aluminum foil and cook until rice is soft, adding more water as needed to keep mixture moist, 10 to 15 minutes more. Remove skillet from oven and set aside to cool slightly, 5 to 10 minutes.