Heat the olive oil in a soup pot over medium-high heat. Add the celery, carrots, and onion, and sauté for 5 to 7 minutes, stirring occasionally.
Add the garlic and flour, cooking for about one minute while stirring.
Gradually pour in the chicken broth, stirring and scraping up any browned bits from the bottom of the pot until the flour has fully dissolved.
Mix in the Italian seasoning, rice, and cream. Raise the heat to high, and once the soup reaches a gentle boil, stir well. Then lower the heat to a simmer, partially cover the pot with the lid slightly ajar, and cook for 10 minutes. Stir occasionally to prevent the rice from sticking to the bottom.
Add the chicken pieces and continue cooking for another 7 to 10 minutes, or until both the chicken and rice are fully cooked. Season generously with salt and pepper to taste.
This soup thickens quickly as the rice absorbs the broth, so you might want to add more chicken broth if you prefer a thinner consistency. For leftovers, you will likely need to add broth as well. If you don’t plan to eat the soup immediately, cook the rice separately and add it to individual servings just before serving.