  We generalize Yau's estimates for the complex Monge-Ampere equation on
compact manifolds in the case when the background metric is no longer Kahler.
We prove $C^{\infty}$ a priori estimates for a solution of the complex
Monge-Ampere equation when the background metric is Hermitian (in complex
dimension two) or balanced (in higher dimensions), giving an alternative proof
of a theorem of Cherrier. We relate this to recent results of Guan-Li.
