  We continue our study of the large N phase transition in q-deformed
Yang-Mills theory on the sphere and its role in connecting topological strings
to black hole entropy. We study in detail the chiral theory defined in terms of
uncoupled single U(N) representations at large N and write down the resulting
partition function by means of the topological vertex. The emergent toric
geometry has three Kaehler parameters, one of which corresponds to the expected
fibration over the sphere. By taking a suitable double-scaling limit we recover
the chiral Gross-Taylor string expansion. To analyse the phase transition we
construct a matrix model which describes the chiral gauge theory. It has three
distinct phases, one of which should be described by the closed topological
string expansion. We verify this expectation by explicit comparison between the
matrix model and the chiral topological string free energies. We also show that
the critical point in the pertinent phase of the matrix model corresponds to a
divergence of the topological string perturbation series.
