Mix together the cream of chicken soup and milk in a small bowl. Pour enough of the soup into a slow cooker to cover the bottom.
Layer chicken breasts over the sauce.
Cover with slices of ham and then Swiss cheese.
Pour the remaining soup over the layers, stirring a little to distribute between layers.
Sprinkle the stuffing on top, and drizzle butter over stuffing.
Cover, and cook on Low for 4 to 6 hours, or 2 to 3 hours on High.
