Put the rice in a large bowl and cover with very hot water. Let it soak anywhere from 5 to 10 minutes. Drain, rinse with cold water and drain again.
Heat 3 tablespoons oil in a large saucepan, add the rice and fry over high heat, stirring softly for 1 to 2 minutes. Add the 1/2 cup chopped onion and stir, from time to time, until the rice begins to change its color to milky white and it sounds and feels heavier, as if it were grains of sand, about 5 more minutes.
Add the chicken stock, 1 stalk celery, sprig parsley, lime juice, 1 teaspoon salt and chile to the rice. When the mixture starts to boil, cover the pot, reduce the heat to lowest setting and cook until the rice is cooked through and the liquid has been absorbed, about 20 minutes.
If the rice grains don't seem soft and cooked through, add a bit more chicken stock or water and let it cook for another 5 more minutes or so. Remove the pan from the heat and let it sit covered for 5 to 10 minutes. Fluff with a fork and set aside.
Cook's Note: The skin of the plantain should be almost entirely black when it is mature and ready to use.
Peel the plantains and slice them diagonally into 1/4-inch thick slices.
In a saute pan over medium heat, add about 1/4-inch of oil. Heat the oil until hot but not smoking. Add the plantain slices and fry until lightly browned, but not blackened, about 2 minutes. Remove the plantains from the oil to a plate covered with paper towels, to drain.
Transfer the rice to a large serving bowl and arrange the hot plantains on top. Garnish with a good dollop of sour cream and serve.
Basic Mexican Chicken Stock:
Put the chicken, carrots, 1 onion, 2 celery stalks, garlic, peppercorns and parsley in a large pot and add enough water to cover the ingredients by at least 3 to 4 inches. Bring the water to a simmer over medium-low heat. Skim off any foam and let the stock simmer for 2 hours. Add the 2 tablespoons salt in the last half hour of cooking. Remove the stock from the heat and set aside. Once the stock has cooled down, strain into a large bowl.
The chicken stock can be kept in the refrigerator for up to 4 days. If you want to keep it longer, it needs to be brought to a boil and simmered for about 10 minutes. Let it cool down and refrigerate again. It can also be frozen for months. The chicken can be shredded and used for multiple purposes such as Tinga, tacos, salads or sandwiches.
Yield: about 6 cups of stock and 6 cups of shredded chicken