Blend the softened butter with parsley, chives, pepper, and salt. Divide into 4 portions and chill until firm.
Flatten each chicken breast half to about 1/4-inch thickness by pounding each between wax paper or plastic wrap.
Place a portion of the chilled butter mixture in the center of each flattened chicken breast half. Roll each to completely enclose the butter. Dust each roll in flour then dip in beaten egg and water. Roll in bread crumbs then place in lightly greased baking dish.
Cover with foil and bake at 350° oven for 45 minutes.
Uncover and bake 15 minutes longer.