The cross section for the elastic scattering reaction νe + e − → νe + e − was measured by the Liquid Scintillator Neutrino Detector using a µ + decay-at-rest νe beam at the Los Alamos Neutron Science Center. The standard model of electroweak physics predicts a large destructive interference between the charge current and neutral current channels for this reaction. The measured cross section, σ νee − = [10.1 ± 1.1(stat.) ± 1.0(syst.)] × Eν e (MeV) ×10 −45 cm 2 , agrees well with standard model expectations. The measured value of the interference parameter, I = −1.01 ± 0.13(stat.) ± 0.12(syst.), is in good agreement with the standard model expectation of I SM = −1.09. Limits are placed on neutrino flavorchanging neutral currents. An upper limit on the muon-neutrino magnetic moment of 6.8 × 10 −10 µ Bohr is obtained using the νµ andνµ fluxes from π + and µ + decay.