For a lighter version of this soup, use half & half instead of the cream. Slideshow: More Chicken Soup Recipes
In a bowl, toss the chicken with the flour, 1/2 teaspoon salt, and 1/4 teaspoon pepper.
In a large heavy pot, heat the butter over medium high heat until hot. Stir in the chicken and brown, in batches if necessary, about 6 minutes per batch. Transfer the chicken to a plate as browned.
Stir the onions, carrots, celery, and 1/4 teaspoon each salt and pepper into the pot and cook, stirring occasionally, until golden, about 6 minutes. Stir in the stock, pasta and the chicken with any accumulated juices and bring to a gentle boil. Cook until the chicken is cooked through, and the pasta is ardent, 12 to 15 minutes. Stir in the cream and season with salt and pepper to taste. Serve.