Rinse the chicken pieces under cold running water and pat dry with paper towels. Place the chicken on a cutting board and season with 1 teaspoon of the salt and 1/4 teaspoon of the ground pepper. Wash your hands well with warm, soapy water.
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Heat the oil in a large, heavy pot over medium-high heat until it is hot but not smoking. Using long-handled tongs, add the chicken pieces to the pot and cook, turning occasionally with the tongs, until browned on all sides, about 8 minutes. Be very careful hereóhot oil splatters!
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Add the sausage and cook, stirring occasionally, until browned, about 2 minutes.
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Add the onion, celery, bell peppers, garlic, bay leaves, thyme, the remaining 1 teaspoon of salt, and the remaining 1/4 teaspoon of ground pepper, and stir well. Cook, stirring occasionally, until soft, about 6 minutes.
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Add the tomatoes, rice, water, and chicken stock, and stir well. Bring to a boil. Reduce the heat to medium-low, cover, and simmer without stirring for 30 minutes.
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Using oven mitts or pot holders, remove the pot from the heat and let rest. You must let this rest, covered, for at least 10 minutes before serving. This ensures that the rice fully absorbs the liquid and is nice and fluffy.
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Yield; 8 to 12 servings