In a large, heavy-bottomed pot over medium-high heat, add 1 tablespoon oil. Add the chicken, season lightly with salt and pepper, and brown on both sides, about 7 minutes, working in batches if necessary. Remove the chicken to a plate. Add the remaining tablespoon of oil and the onions, peppers, and celery, and cook until the vegetables are soft, about 5 minutes. Add the garlic, Cajun seasoning, cayenne, salt and pepper, and give it a stir. Stir in the rice. Add the chicken back to the pot, along with the broth and tomatoes, and season with salt and pepper. Bring to a boil, cover, and reduce the heat to a simmer. Cook until the liquid is absorbed and the rice is tender, about 30 minutes. (Reserve 3 cups rice mixture for another use, such as Round 2 Recipe Cajun Quesadillas and Online Round 2 Recipe Cajun Red Bean and Rice Soup.) Serve, garnished with parsley.