Heat a large pot or Dutch oven over medium heat. Add the onion, celery, carrot, and garlic, and sauté until they begin to soften.
Add the chicken, then sprinkle in the spices and pour in the broth. Cover and simmer over medium-low heat for 25–30 minutes, until the chicken is cooked through and shreds evenly.
Remove the chicken from the pot, shred it, and return it to the broth.
Rinse the rice in a fine mesh strainer under cold water for about one minute, until the water runs clear. Do not skip this step: it helps remove excess starch so the soup stays smooth instead of thick and clumpy.
Add the rinsed rice to the pot. Cover and cook over low heat for 10–15 minutes, until the rice is tender.
Add salt and pepper to taste before serving.