Summary: An exact conformal field theory describing a black hole in two-dimensional spacetime is found as an \(\text{SL}(2,{\mathbf R})/\text{U}(1)\) gauged Wess-Zumino-Witten model. For \(k=\frac 94\), the conformal field theory can be regarded as a classical solution of the same system that is probed in the \(c=1\) matrix model. The conformal field theory govering the spacetime is regular at the Riemannian singularity, but it appears that generic perturbations blow up there. It is argued that the end point of the Hawking black hole evaporation is the standard spacetime of the \(c=1\) matrix model, which should be regarded as an analogue of the extremee Reissner-Nordström black hole of four-dimensional general relativity. The \(c=1\) model is thus a model of the quantum mechanics of matter interacting with a black hole.