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A search for the rare two-body charmless baryonic decay B+ -> p (Lambda) over bar is performed with pp collision data, corresponding to an integrated luminosity of 3 fb(-1), collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. An excess of B+ -> p (Lambda) over bar 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+ -> K-S(0)pi(+) decay for normalisation, is B(B+ -> p (Lambda) over bar) = (2.4(-0.8)(+)(+1.0) +/- 0.3) x 10(-7), where the first uncertainty is statistical and the second systematic.