We present a limit on the branching fraction for the decay B0-->gammagamma 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 21.3x10(6) e+e--->Upsilon(4S)-->BB decays, we establish an upper limit on the branching fraction of B(B0-->gammagamma)<1.7x10(-6) at the 90% confidence level. This result substantially improves upon existing limits.