Let (M, h) be a compact 4-dimensional Einstein manifold, and suppose that h is Hermitian with respect to some complex structure J on M . Then either (M, J, h) is Kaehler-Einstein, or else, up to rescaling and isometry, it is one of the following two exceptions: the Page metric on CP2 # CP2 or the Chen-LeBrun-Weber metric on CP2 # 2 CP2 . Ideas used in proving this uniqueness result also lead to a new proof of the existence of these exceptional metrics.