A matrix model is constructed which describes a chiral version of the
large N U(N) gauge theory on a two-dimensional sphere of area A. This
theory has three separate phases. The large area phase describes the a
ssociated chiral string theory. An exact expression for the free energ
y in the large area phase is used to derive a remarkably simple formul
a for the number of topologically inequivalent covering maps of a sphe
re with fixed branch points and degree n.