1. Heat the olive oil in a large soup pot over medium-high heat. Add the celery, carrots, and onion, then cook for 5 to 7 minutes, stirring occasionally, until the vegetables begin to soften.

2. Add the garlic and flour. Stir well and cook for about 1 minute to remove the raw flour taste.

3. Slowly pour in the chicken broth while stirring, scraping the bottom of the pot to loosen any flavorful bits. Continue stirring until the flour is fully blended into the broth.

4. Add the Italian seasoning, rice, and heavy cream. Bring the soup to a gentle boil, then stir well. Reduce the heat to a simmer and cover the pot with the lid slightly open. Cook for 10 minutes, stirring occasionally so the rice does not stick.

5. Add the chicken pieces and simmer for 7 to 10 more minutes, or until the chicken is cooked through and the rice is tender. Season with salt and black pepper to taste.

6. Serve warm. For a thinner soup, stir in extra chicken broth as needed.