  We investigate the string theory on three dimensional black holes discovered
by Ba\~{n}ados, Teitelboim and Zanelli in the framework of conformal field
theory. The model is described by an orbifold of the $\widetilde{SL}(2,R)$ WZW
model. The spectrum is analyzed by solving the level matching condition and we
obtain winding modes. We then study the ghost problem and show explicit
examples of physical states with negative norms. We discuss the tachyon
propagation and the target space geometry, which are irrelevant to the details
of the spectrum. We find a self-dual T-duality transformation reversing the
black hole mass. We also discuss difficulties in string theory on curved
spacetime and possibilities to obtain a sensible string theory on three
dimensional black holes. This work is the first attempt to quantize a string
theory in a black hole background with an infinite number of propagating modes.
