Coat the bottom of a large heavy-bottom saucepan with the vegetable oil. Add the onion, garlic, red pepper and zucchini to the pan. Cook over low heat, stirring occasionally, until the vegetables are very soft, about 5 minutes. Add the chicken and turn the heat up to medium-high. Stir until the chicken is cooked lightly on all sides. Add the tomatoes, rice, chicken broth and salt. Bring the broth to a boil and then adjust the heat to maintain a slow simmer. Let the casserole simmer until the rice is tender, about 45 minutes. Stir in the pepper and the parsley and serve.