1. Boil chicken breasts for 50 minutes, or until cooked through.
2. Place on a platter to cool, and reserve broth.
3. Prepare stuffing mix according to package directions.
4. Spread in a 9x13 baking dish.
5. When chicken cools,remove skin and tear into medium strips.
6. Layer on prepared stuffing.
7. In a 2 quart.
8. saucepan,melt remaining 1 stick of butter;blend in flour and seasonings with a whisk,about 3 minutes.
9. Add reserved broth slowly,and cook and stir until mixture thickens.
10. Stir a small amount of the hot mixture into the beaten eggs,then pour the eggs into the hot mixture,and pour over the chicken and stuffing.
11. Bake in a 325 oven for 1 hour,or until knife inserted in the center comes out clean.
12. Let stand at least 5 minutes before serving.
13. Serve with mushroom sauce.