  Collective neutrino flavor transformations deep inside a supernova are
sensitive to the neutrino mass hierarchy even at extremely small values of
theta(13). Exploiting this effect, we show that comparison of the antineutrino
signals from a galactic supernova in two megaton class water Cherenkov
detectors, one of which is shadowed by the Earth, will enable us to distinguish
between the hierarchies if sin^2 theta(13) < 10^{-5}. On the other hand, the
observation of Earth effects in the inverted hierarchy for sin^2 theta(13) >
10^{-3} will provide a robust observable signature of collective oscillations
occurring deep inside the supernova.
