  The T2K off-axis near detector, ND280, is used to make the first differential
cross-section measurements of electron neutrino charged current interactions at
energies ~1 GeV as a function of electron momentum, electron scattering angle
and four-momentum transfer of the interaction. The total flux-averaged $\nu_e$
charged current cross-section on carbon is measured to be
$1.11\pm0.09~(stat)\pm0.18~(syst)\times10^{-38} cm^2/nucleon$. The differential
and total cross-section measurements agree with the predictions of two leading
neutrino interaction generators, NEUT and GENIE. The NEUT prediction is
$1.23\times10^{-38} cm^2/nucleon$ and the GENIE prediction is
$1.08\times10^{-38} cm^2/nucleon$. The total $\nu_e$ charged current
cross-section result is also in agreement with data from the Gargamelle
experiment.
