  We present a limit on the branching fraction for the decay $B^0 \to \gamma
\gamma$ using data collected at the $\Upsilon(4S)$ resonance with the BABAR
detector at the PEP-II asymmetric--energy $e^+e^-$ collider. Based on the
observation of one event in the signal region, out of a sample of $21.3 \times
10^6$ $e^+e^- \to \Upsilon(4S) \to B\bar B$ decays, we establish an upper limit
on the branching fraction of ${\cal B}(B^0 \to \gamma \gamma) < 1.7 \times
10^{-6}$ at the 90% confidence level. This result substantially improves upon
existing limits.
