  We find evidence for the semileptonic baryonic decay $B^-\to p\bar
p\ell^-\bar\nu_\ell$ ($\ell=e,\mu$), based on a data sample of 772 million
$B\bar B$ 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 $B^-\to p\bar p\ell^-\bar\nu_\ell$ is measured to be
$(5.8^{+2.4}_{-2.1}\textrm{(stat.)}\pm 0.9\textrm{(syst.)})\times 10^{-6}$ with
a significance of 3.2$\sigma$, where lepton universality is assumed. We also
estimate the corresponding upper limit: $\mathcal{B}(B^-\to p\bar
p\ell^-\bar\nu_\ell) < 9.6\times 10^{-6}$ at the 90% confidence level. This
measurement helps constrain the baryonic transition form factor in B decays.
