1. In a 5 quart Dutch oven or larger pot over medium heat, sauté onion and celery until softened almost softened; add carrot and cook another 5 minutes, add broth, water and chicken. Bring just to boiling, then stir in rice, reserving seasoning packet. Cover and remove from heat.
2. In a small bowl, combine salt, pepper and flour. In a medium saucepan over medium heat, melt butter. Stir in contents of seasoning packet until mixture is bubbly. Reduce heat to low, then stir in flour mixture by tablespoons, to form a roux. Whisk in cream, milk, and half and half a little at a time, until fully incorporated and smooth. Cook until thickened, 5 minutes.
3. Stir cream mixture into broth and rice. Cook over medium heat until heated through, 10 to 15 minutes.