Rinse the rice and place in a bowl. Cover with warm water and let it soak for 15 minutes.
While the rice is soaking, season the chicken with salt and pepper. Heat the oil in a large cazuela or pot. Once the oil is hot, add the chicken pieces and cook for 5 minutes per side. Remove from the pot and set aside.
Now it is time to cook the rice. Drain the rice using a strainer and shake to make sure it doesn’t have any excess moisture. Before adding the rice to the cazuela, make sure that there is only about one tablespoon of oil in it. If you see more oil or fat from the chicken in the cazuela, remove it, since too much oil will render a mushy rice. Now, stir in the rice and cook over medium high heat for 3 minutes.
Add the diced carrots and the chopped onions. Cook for 3 more minutes.
Place the chopped tomato and garlic in your blender along with ¾ cups of warm water and process until smooth.
Pour this mixture over the rice and let it cook for a couple of minutes. Once it starts boiling, reduce the heat, season with salt, add the chicken pieces, and cover the pot. Cook for 1 minute, then add the cilantro sprigs and the drained green peas (see note above). Keep cooking for 6-8 more minutes.
After you are done cooking, remove the Arroz con Pollo pot from the heat and let it rest for 12-15 more minutes. Some cooks cover the pot with a kitchen towel in order to absorb all the moisture from the rice.