  The quantum stress tensor $<T_{\mu\nu}>$ is calculated in the 2+1 dimensional
black hole found by Banados, Teitelboim, and Zanelli. The Greens function, from
which $<T_{\mu\nu}> $ is derived, is obtained by the method of images. For the
non-rotating black hole, it is shown that $<T_{\mu\nu}>$ is finite on the event
horizon, but diverges at the singularity. For the rotating solution, the stress
tensor is finite at the outer horizon, but diverges near the inner horizon.
This suggests that the inner horizon is quantum mechanically unstable against
the formation of a singularity.
