  We search for the rare flavor-changing neutral current process $B^- \to
\Lambda {\overline p} \nu{\overline{\nu}}$ using data from the BABAR
experiment. A total of 424 fb$^{-1}$ of $e^+e^-$ collision data collected at
the center-of-mass energy of the $\Upsilon$(4S) resonance is used in this
study, corresponding to a sample of ${(471 \pm 3) \times 10^{6}}$
$B\overline{B}$ pairs. Signal $B^- \to \Lambda {\overline p}
\nu{\overline{\nu}}$ candidates are identified by first fully reconstructing a
$B^+$ decay in one of many possible exclusive decays to hadronic final states,
then examining detector activity that is not associated with this reconstructed
$B^+$ decay for evidence of a signal $B^- \to \Lambda {\overline p}
\nu{\overline{\nu}}$ decay. The data yield is found to be consistent with the
expected background contribution under a null signal hypothesis, resulting in
an upper limit of ${{\cal B} (B^- \to \Lambda {\overline p}
\nu{\overline{\nu}}) < 3.0\times 10^{-5}}$ at the $90\%$ confidence level.
