Slightly flatten chicken breasts with a tenderizing mallet between sheets of plastic wrap. Lightly season with salt and pepper and brush with some beaten egg.
Place crab meat stuffing in the middle of the chicken breasts and roll the breasts around the stuffing. Cover and let sit in fridge until well chilled. Bread the breasts by coating them with the rest of the egg, the flour and the bread crumbs. Saute until done. Serve with sour cream.