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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 ν(e) charged current cross section on carbon is measured to be ⟨σ⟩(ϕ)=1.11±0.10(stat)±0.18(syst)×10⁻³⁸ cm²/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 1.23×10⁻³⁸ cm²/nucleon and the GENIE prediction is 1.08×10⁻³⁸ cm²/nucleon. The total ν(e) charged current cross-section result is also in agreement with data from the Gargamelle experiment.