  We show that on a smooth Hermitian minimal model of general type the
Chern-Ricci flow converges to a closed positive current on M. Moreover, the
flow converges smoothly to a Kahler-Einstein metric on compact sets away from
the null locus of K_M. This generalizes work of Tsuji and Tian-Zhang to
Hermitian manifolds, providing further evidence that the Chern-Ricci flow is a
natural generalization of the Kahler-Ricci flow.
