Melt one tablespoon of butter in a large pot or Dutch oven over medium heat.
Add the onion, celery, and carrots. Cook and stir for 5 minutes until the vegetables start to soften.
Add the chicken stock, rice, and seasoning packet from the rice box. Cover and simmer for 10 minutes over low heat.
While the soup is simmering, melt the remaining butter in a medium pan. Reduce the heat to low, then whisk in the flour until you have a paste.
Whisk in the heavy cream a little at a time, stirring until smooth before adding more. Cook until the mixture is thickened, about 2-3 minutes.
Stir the cream mixture into the pot with the broth.
Add the diced chicken, cover, and cook over medium-low heat for 8-10 minutes. It will continue to get thicker as it sits.
Season with salt and pepper to taste. Serve immediately.