  The results of a search for the rare two-body charmless baryonic decays $B^0
\to p \bar{p}$ and $B_s^0 \to p \bar{p}$ are reported. The analysis uses a data
sample, corresponding to an integrated luminosity of 0.9 fb$^{-1}$, of $pp$
collision data collected by the LHCb experiment at a centre-of-mass energy of 7
TeV. An excess of $B^0 \to p \bar{p}$ candidates with respect to background
expectations is seen with a statistical significance of 3.3 standard
deviations. This is the first evidence for a two-body charmless baryonic $B^0$
decay. No significant $B_s^0 \to p \bar{p}$ signal is observed, leading to an
improvement of three orders of magnitude over previous bounds. If the excess
events are interpreted as signal, the 68.3% confidence level intervals on the
branching fractions are {eqnarray} \cal{B}(B^0 \to p \bar{p}) & = & (1.47
\,^{+0.62}_{-0.51} \,^{+0.35}_{-0.14}) \times 10^{-8} \,, *{0.3cm}
\cal{B}(B_s^0 \to p \bar{p}) & = & (2.84 \,^{+2.03}_{-1.68} \,^{+0.85}_{-0.18})
\times 10^{-8} \,, {eqnarray} where the first uncertainty is statistical and
the second is systematic.
