In a large, deep frying pan, heat the oil over moderately high heat. Season the chicken with 1/4 teaspoon each of the salt and pepper. Cook the chicken, turning, until well browned, about 8 minutes in all. Remove. Pour off all but 2 tablespoons of the fat from the pan. Reduce the heat to moderately low. Add the onion, and garlic to the pan and cook, stirring occasionally, until the onion starts to soften, about 2 minutes. Add the bell peppers and cook, stirring occasionally, until they start to soften, about 3 minutes longer. Add the tomatoes, broth, and the remaining 1 3/4 teaspoons salt and 1/4 teaspoon of the pepper and bring to a simmer. Stir in the rice and add the chicken in an even layer. Simmer, partially covered, over moderately low heat until the chicken and rice are just done, 20 to 25 minutes. Sprinkle with parsley.