  We examine the prospects for detecting supernova $\nu_e$ in JUNO, RENO-50,
LENA, or other approved or proposed large liquid scintillator detectors. The
main detection channels for supernova $\nu_e$ in a liquid scintillator are its
elastic scattering with electrons and its charged-current interaction with the
$^{12}$C nucleus. In existing scintillator detectors, the numbers of events
from these interactions are too small to be very useful. However, at the
20-kton scale planned for the new detectors, these channels become powerful
tools for probing the $\nu_e$ emission. We find that the $\nu_e$ spectrum can
be well measured, to better than $\sim 40\%$ precision for the total energy and
better than $\sim 25\%$ precision for the average energy. This is adequate to
distinguish even close average energies, e.g., 11 MeV and 14 MeV, which will
test the predictions of supernova models. In addition, it will help set
constraints on neutrino mixing effects in supernovae by testing non-thermal
spectra. Without such large liquid scintillator detectors (or Super-Kamiokande
with added gadolinium, which has similar capabilities), supernova $\nu_e$ will
be measured poorly, holding back progress on understanding supernovae,
neutrinos, and possible new physics.
