  Upper limits are presented on the diffuse flux of ultra-high energy $\nu_e$,
based on analysis of data taken by the RICE experiment during August, 2000. The
RICE receiver array at South Pole monitors cold ice for radio-wavelength
Cherenkov radiation resulting from neutrino-induced in-ice showers. For
energies above 1 EeV, RICE is an effective detector of over 15 km$^3$ sr.
Potential signal events are separated from backgrounds using vertex location,
event reconstruction, and signal shape. These are the first terrestrial limits
exploiting the physics of radio Cherenkov emissions from charged-current
$\nu_e+N\to e+N'$ interactions.
