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.