We present a new third-order essentially non-oscillatory central scheme for approximating solutions of two-dimensional hyperbolic conservation laws. Our scheme is based on a two-dimensional extension of the centered weighted essentially non-oscillatory (CWENO) reconstruction we presented in [Levy, Puppo, Russo, Central Weno Schemes for Hyperbolic Systems of Conservation Laws, Math. Mode. and Nume. Anal.]. This is a ``true'' 2D method; it is not based on a direction-by-direction approach. Our method is formalized in terms of a black box which needs as an input only the specific flux. The numerical results we present support our expectations for a robust and high-resolution method.