  We present the result of a search for the charmless two-body baryonic decay
B^0 -> ppbar in a sample of 88 million Y(4S) -> BBbar decays collected by the
BaBar detector at the SLAC PEP-II asymmetric-energy $B$ Factory. We use
Cherenkov radiation to identify protons cleanly, and determine the signal yield
with a maximum-likelihood fit technique using kinematic and topological
information. We find no evidence for a signal and place a 90% confidence-level
upper limit of BF(B^0 -> ppbar) < 2.7 x 10^-7.
