Heat the olive oil in a large pot over medium-high heat. Add the diced celery, carrots, and onion and sauté for 5-7 minutes, or until softened and aromatic.
Stir in the minced garlic and flour. Cook for about 1 minute, stirring constantly, to create a roux.
Slowly pour in the chicken broth while stirring continuously. Scrape up any browned bits from the bottom of the pot. Continue stirring until the flour is fully dissolved.
Add the Italian seasoning and long-grain white rice to the pot. Stir well to combine all ingredients.
Pour in the heavy cream and increase the heat to bring the soup to a boil.
Once boiling, reduce the heat to low, cover the pot with the lid slightly ajar to allow steam to escape, and simmer for 10 minutes, stirring occasionally to prevent sticking.
Add the cooked chicken to the soup and continue cooking for another 7-10 minutes, or until the rice and chicken are fully cooked and tender.
Season with salt and pepper to taste. Garnish with fresh parsley, if desired.
Serve and enjoy!