In a large Dutch oven or soup pot, heat the olive oil over medium-high heat. Add the carrots, onions, celery, and garlic, and sauté for 5 minutes until the vegetables are tender.
Cook the soup:
Add the seasonings, broth, water, and shredded chicken. Bring the soup to a boil, add the rice, stir, and reduce the heat to low. Simmer for 20 to 25 minutes until the rice is tender. If using brown rice, simmer for 45 to 50 minutes.
Serve:
Before serving, pour the lemon juice into the soup and stir to combine. Turn off the heat and ladle the soup into bowls.