  We report the result of a search for the rare decay B^0 -> gamma gamma in 426
fb-1 of data, corresponding to 226 million B^0 \bar{B}^0 pairs, collected on
the Upsilon(4S) resonance at the PEP-II asymmetric-energy e+e- collider using
the BABAR detector. We use a maximum likelihood fit to extract the signal yield
and observe 21^{+13}_{-12} signal events with statistical significance of 1.9
sigma. This corresponds to a branching fraction B(B^0 -> gamma gamma) = (1.7 +-
1.1(stat.) +- 0.2(syst.)) x 10^-7. Based on this result, we set a 90%
confidence level upper limit of B(B^0 -> gamma gamma) < 3.3 x 10^-7.
