  A search for the rare two-body charmless baryonic decay $B^+ \to p
\bar\Lambda$ is performed with $pp$ collision data, corresponding to an
integrated luminosity of $3\,\mbox{fb}^{-1}$, collected by the LHCb experiment
at centre-of-mass energies of 7 and 8 TeV. An excess of $B^+ \to p \bar\Lambda$
candidates with respect to background expectations is seen with a statistical
significance of 4.1 standard deviations, and constitutes the first evidence for
this decay. The branching fraction, measured using the $B^+ \to K^0_{\mathrm S}
\pi^+$ decay for normalisation, is \begin{eqnarray} \mathcal{B}(B^+ \to p
\bar\Lambda) & = & ( 2.4 \,^{+1.0}_{-0.8} \pm 0.3 ) \times 10^{-7} \,,
\nonumber \end{eqnarray} where the first uncertainty is statistical and the
second systematic.
