In this note, we show that the regularity results of [4] generalize to Monge-Ampre equations on the class of compact Hessian manifolds. We prove C^2, regularity of locally convex viscosity solutions, which rules out the possibility of Pogorelov-type counterexamples on this class of manifolds. We also derive some a priori estimates, from which follow some existence theorems with minimal regularity assumptions, generalizing results in [7] and [11].