In a large pot or dutch oven, over medium heat, combine broth and chicken. Bring to a boil, then stir in rice. Cover and remove from heat. Set aside.
In a medium saucepan or large, deep skillet over medium heat, add olive oil.
Add diced onion, carrots and celery. Season with salt and pepper and sauté for about 5 minutes. If the rice contained a seasoning packet, stir it in now and cook the veggies for another 5 minutes.
Gradually add the flour to the veggies, while constantly stirring to form a roux.
Sauté roux for 3-4 minutes and gradually, over low-medium heat, start whisking in the cream, until fully incorporated and smooth. Cook until thickened, about 5 minutes.
Bring back the pot with chicken and rice, place it over low-medium heat and stir cream mixture into the broth and rice. Cook over medium heat until heated through and the rice is done, 15-20 minutes.
If you want the soup to be creamier, blend half of it using an immersion blender. Or add 1/2 to a large blender and puree soup until there are no large chunks left.
Garnish with fresh chopped parsley.