In a large stockpot or Dutch oven, saute onion and celery in the olive oil over medium heat. Sprinkle 1 teaspoon of salt over the vegetables and stir while cooking. Cook until onions are soft and translucent and some caramelization begins to show on the vegetables.
Add carrots, chicken pieces, pepper, and herbs.
Cover the contents in the poot with chicken broth/water. Bring to a boil over high heat. Then, reduce to a simmer and cover with a lid.
Simmer the chicken for at least 30 minutes, which will give the flavors enough time to blend and add richness and depth to the soup broth.
Remove chicken (bones and skin included) from the pot and set aside.
Add the rice to the soup mixture and continue simmering, lid on, for about 10 minutes longer, until the rice has softened and is cooked through.
Meanwhile, separate the chicken meat from the bones and skin. Discard bones and skin. Shred or chop the chicken and return it to the pot to continue simmering for the remainder of the time it takes for the rice to cook.
Stir the soup, season with salt and pepper to taste, and serve.