Start by making Lynda's Chicken Broth.
Add potatoes, carrots, and celery to a pot, and add enough chicken stock to cover, and bring to a boil over high heat. Reduce heat to medium high and cook about 20 minutes or until tender.
While vegetables are cooking, in a separate pot, melt the butter and stir in the flour over medium heat. Cook 5 minutes, stirring constantly. Don't let it burn. Add enough of the reserved chicken broth, stirring constantly to make a very thick sauce. Then add the cooked vegetables with the broth they have cooked in. Stir really well and the broth will thin down the sauce to a gravy-like consistency. Add more broth, if necessary, to achieve the consistency of the sauce desired.
Simmer 5 minutes and add salt and pepper to taste. Add chicken at the end and heat through.