We find evidence for the semileptonic baryonic decay B- -> p (p) over barl(-)(nu) over bar (l) (l = e, mu), based on a data sample of 772 million B (B) over bar pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy electron-positron collider. A neural-network based hadronic B-meson tagging method is used in this study. The branching fraction of B- -> p (p) over barl(-)(nu) over bar (l) is measured to be (5.8(-2.1)(+2.4)(stat) +/- 0.9(syst)) x 10(-6) with a significance of 3.2 sigma s, where lepton universality is assumed. We also estimate the corresponding upper limit: B(B- -> p (p) over barl(-)(nu) over bar (l)) < 9.6 x 10(-6) at the 90% confidence level. This measurement helps constrain the baryonic transition form factor in B decays.