  We present a search for the decay B^0 --> pi^0 pi^0 by the BABAR experiment
at the PEP-II asymmetric-energy B-factory at SLAC. Using approximately 88
million B bar{B} pairs collected between 1999 and 2002, we place a 90%
confidence level upper limit on the branching fraction of B(B^0 --> pi^0 pi^0)
< 3.6 times 10^{-6}. This result is preliminary.
