1. Place the chicken breasts in a small kettle and add chicken broth barely to cover. Bring to a boil, reduce the heat, cover and simmer gently until the meat is tender, twenty-five to forty minutes, depending on the size of the breasts. Remove the chicken from the broth and cool. Carefully remove skin and the meat from the bones.
2. Preheat oven to hot (400° F.).
3. Cut six pieces of aluminum foil large enough to make an envelope for each breast half and spread the foil with half the butter.
4. In a saucepan melt the remaining butter, add the flour and stir with a wire whisk until blended. Meanwhile, bring the milk, wine and one-half cup of the chicken broth to a boil and add all at once to the butter-flour mixture, stirring vigorously with the whisk until the sauce is thickened and smooth. Add the egg yolk lightly beaten with a little of the hot sauce, stirring gently until thickened. Do not let boil. Add the seasonings and stir in the mushrooms and chives.
5. Place half a chicken breast in the center of each square of aluminum foil and spoon some sauce over the top. Fold the edges of the foil and seal tightly by crimping the edges. Arrange on baking sheet and bake ten minutes.