First Search for the Flavor Changing Neutral Current Decay D^0 -> gamma gamma

Using 13.8 fb^{-1} of data collected at or just below the Upsilon(4S) with the CLEO detector, we report the result of a search for the flavor changing neutral current process D^{0} to gammagamma. We observe no significant signal for this decay mode and determine 90% confidence level upper limits on the branching fractions Br(D^{0}to gammagamma)/Br(D^{0}topi^{0}pi^{0}) < 0.033 and Br(D^{0}togammagamma) < 2.9 times 10^{-5}.