  We present the results of a time-coincident event search for low-energy
electron antineutrinos in the KamLAND detector with gamma-ray bursts from the
Gamma-ray Coordinates Network and Fermi Gamma-ray Burst Monitor. Using a
variable coincidence time window of $\pm$500s plus the duration of each
gamma-ray burst, no statistically significant excess above background is
observed. We place the world's most stringent 90% confidence level upper limit
on the electron antineutrino fluence below 17.5 MeV. Assuming a Fermi-Dirac
neutrino energy spectrum from the gamma-ray burst source, we use the available
redshift data to constrain the electron antineutrino luminosity and effective
temperature.
