We study the relation between the SL(2, R)/U(1) black hole and c = 1 Liouville theory. A deformation, which interpolates the BRST operators of both models, is explicitly constructed. This interpolation is isomorphic, and the physical spectrum of the black hole is equivalent to that of the c = 1 model tensored by a topological U(1)/U(1) model. Some implications of the deformation are discussed.