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 νe charged current cross-section on carbon is measured to be σ φ = 1.11 ± 0.09 (stat) ± 0.18 (syst) × 10 −38 cm 2 /nucleon. The differential and total crosssection measurements agree with the predictions of two leading neutrino interaction generators, 3 NEUT and GENIE. The NEUT prediction is 1.23 × 10 −38 cm 2 /nucleon and the GENIE prediction is 1.08 × 10 −38 cm 2 /nucleon. The total νe charged current cross-section result is also in agreement with data from the Gargamelle experiment.PACS numbers: 14.60. Pq, 14.60.Lm, 25.30.Pt, 29.40.Ka Introduction-T2K is a long baseline neutrino oscillation experiment measuring ν e appearance and ν µ disappearance from a ν µ beam. Neutrino oscillations are described by a mixing matrix parametrized by three mixing angles and a CP violating phase, δ CP [1,2]. The three mixing angles have been measured to better than 10% precision [3], and measuring δ CP is currently a major goal in neutrino physics [4].Future ν e appearance measurements can be used to search for CP violation in neutrino interactions, and these rely on precise understanding of both ν µ and ν e charged-current (CC) interaction cross-sections at energies ∼1 GeV. Many ν µ cross-section measurements have been made at the GeV scale, both of the total CC inclusive cross-section and of individual interaction modes (see Ref.[5] for a review of cross-section data, and Refs. [6][7][8] for recent results). Only the Gargamelle experiment has measured the ν e CC inclusive cross-section at the GeV scale [9], and there are currently no ν e differential crosssection results as a function of the electron kinematics. Theoretical differences are expected between ν e and ν µ cross-sections [10], and measuring these with data is critical to understand the systematic uncertainties related to the search for CP violation in the lepton sector. The uncertainty in ν e cross-sections will become increasingly important in future oscillation experiments as statistical and other systematic uncertainties are reduced.In this Letter we present the first ν e CC inclusive differential cross-section measurements for neutrinos with energy ∼1 GeV as a function of the electron momentum (p e ), electron scattering angle (cos(θ e )) and the fourmomentum transfer of the interaction (Q 2 ). The total flux-averaged CC inclusive cross-section is also presented.T2K Experiment-T2K [11] operates from the J-PARC facility in Tokai, Japan. A muon neutrino beam is produced from the decay of charged pions and kaons generated by 30 GeV proton collisions on a graphite target and focused by three magnetic horns. Downstream of the horns is the decay volume, 96 meters in length, followed by the beam dump and muon monitors (MUMON [12]). The neutrino beam illuminates ...