  The electron-neutrino charged-current quasielastic (CCQE) cross section on
nuclei is an important input parameter for electron neutrino appearance
oscillation experiments. Current experiments typically begin with the muon
neutrino cross section and apply theoretical corrections to obtain a prediction
for the electron neutrino cross section. However, at present no experimental
verification of the estimates for this channel at an energy scale appropriate
to such experiments exists. We present the cross sections for a CCQE-like
process determined using the MINERvA detector, which are the first measurements
of any exclusive reaction in few-GeV electron neutrino interactions. The result
is given as differential cross-sections vs. the electron energy, electron
angle, and square of the four-momentum transferred to the nucleus, $Q^{2}$. We
also compute the ratio to a muon neutrino cross-section in $Q^{2}$ from
MINERvA. We find satisfactory agreement between these measurements and the
predictions of the GENIE generator. We furthermore report on a photon-like
background unpredicted by the generator which we interpret as neutral-coherent
diffractive scattering from hydrogen.
