Three-body B+ -> p (p) over barK(+) and B+ -> p (p) over bar pi(+) decays are studied using a data sample corresponding to an integrated luminosity of 3.0 fb(-1) collected by the LHCb experiment in proton-proton collisions at center-of-mass energies of 7 and 8 TeV. Evidence of CP violation in the B+ -> p (p) over barK(+) decay is found in regions of the phase space, representing the first measurement of this kind for a final state containing baryons. Measurements of the forward-backward asymmetry of the light meson in the p (p) over bar rest frame yield A(FB)(p (p) over barK(+), m(p (p) over bar) < 2.85 GeV/c(2)) = 0.495 +/- 0.012 (stat) +/- 0.007 (syst) and A(FB)(p<(p)over bar>pi(+), m(p (p) over bar) < 2.85 GeV/c(2)) = -0.409 +/- 0.033 (stat) +/- 0.006 (syst). In addition, the branching fraction of the decay B+ -> <(Lambda)over bar>(1520)p is measured to be B(B+ -> (Lambda) over bar (1520)p) = (3.15 +/- 0.48 (stat) +/- 0.07 (syst) +/- 0.26 (BF)) x 10(-7), where BF denotes the uncertainty on secondary branching fractions.