  We show that a large class of supersymmetric compactifications, including all
simply connected Calabi-Yau and G_2 manifolds, have classical configurations
with negative energy density as seen from four dimensions. In fact, the energy
density can be arbitrarily negative -- it is unbounded from below.
Nevertheless, positive energy theorems show that the total ADM energy remains
positive. Physical consequences of the negative energy density include new
thermal instabilities, and possible violations of cosmic censorship.
