Add the olive oil, celery, carrots, and onion to a soup pot over medium-high heat. Sauté for 5-7 minutes, stirring occasionally.
Stir in the garlic and flour and cook for about a minute.
Slowly pour in the broth and stir/scrape up the browned bits from the bottom of the pot until the flour has dissolved.
Stir in the Italian seasoning, rice, and cream. Increase the heat to high, and once the soup comes to a gentle boil, give it a good stir, then reduce the heat so it's simmering and cover the pot with the lid slightly ajar. Simmer the soup for 10 minutes. I stir it every now and then to prevent the rice from sticking to the bottom of the pot.
Add in the chicken and cook for another 7-10 minutes or until the chicken and rice are both cooked. Season with salt & pepper as needed (I am generous with both). This soup will soak up the broth FAST. You may need to add more chicken broth if you prefer a less thick soup, and you'll definitely have to add broth to leftovers. Cook the rice separately if you don't plan on eating it right away (add rice to individual portions just before serving).