  We present results of a search for the rare flavor-changing neutral-current
decay B --> pi l+ l-, based on a data sample corresponding to 209 fb-1 of
integrated luminosity collected with the BABAR detector at the PEP-II B
Factory. We reconstruct the four exclusive B decay modes B+ --> pi+ l+ l- and
B0 --> pi0 l+ l-, where l is either an e or mu. We find no evidence for a
signal, and we obtain the upper limit at 90% confidence level on the
lepton-flavor--averaged branching fraction to be BF(B+ --> pi+ l+ l-) = 2 x
tau_B+/tau_B0 x BF(B0 --> pi0 l+ l-) < 7.9 x 10-8. We also obtain an upper
limit at 90% confidence level on the lepton-flavor--violating decay B --> pi e
mu of BF(B --> pi e mu) < 9.8 x 10-8.
