  We define a functional for Hermitian metrics using the curvature of the Chern
connection. The Euler-Lagrange equation for this functional is an elliptic
equation for Hermitian metrics. Solutions to this equation are related to
K\"ahler-Einstein metrics, and are automatically K\"ahler-Einstein under
certain conditions. Given this, a natural parabolic flow equation arises. We
prove short time existence and regularity results for this flow, as well as
stability for the flow near K\"ahler-Einstein metrics with negative or zero
first Chern class.
