In a 3-quart Dutch oven or pot, melt the butter and saute the chopped carrot, celery, and onion until tender, about 5 minutes
Stir in the rice and pour in the chicken stock, thyme, and parsley. Bring to a boil, reduce the heat to medium-low and simmer for about 15 minutes
In a small bowl, whisk the flour into the evaporated milk and add it to the pot. Bring the soup to a boil, and cook until thickened, about 3 minutes. Season with salt and pepper. Add the cooked chicken and simmer until heated through.