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.
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