  We present an exact operator quantization of the Euclidean Black Hole CFT
using a recently established free field parametrization of the fundamental
fields of the classical theory [4,5,6,7]. Quantizing the map to free fields, we
show that the resulting quantum fields are causal and transform as covariant
fields w.r.t. the Virasoro algebra. We construct the reflection operator of the
quantum theory and demonstrate its unitarity. We furthermore discuss the
W-algebra of the Euclidean Black Hole model. It turns out that unitarity of the
reflection operator is a simple consequence of the fact that certain
representations of the W-algebra are unitarily equivalent.
