The results of a search for the rare two-body charmless baryonic decays B0→pp¯ and B0s→pp¯ 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 B0→pp¯ 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 B0s→pp¯ 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 B(B0→pp¯)=1.47+0.62+0.35−0.51−0.14×10−8,B(Bs→pp¯)=2.84+2.03+0.85−1.68−0.18×10−8, where the first uncertainty is statistical and the second is systematic.