  We present main results of the investigation of the rare decay mode D^0
-->gamma gamma, in which the long distance contributions are expected to be
dominant. Using the Heavy Quark Chiral Lagrangian we have considered the
anomaly contribution which relates to the annihilation part of the weak
Lagrangian and the one - loop pi, K diagrams. The loop contributions which are
proportional to g and contain the a_1 Wilson coefficient are found to dominate
the decay amplitude. The branching ratio is then calculated to be (1.0+-0.5)x
10^{-8}. Observation of an order of magnitude larger branching ratio could
signal new physics.
