  String theory and ``quantum geometry'' have recently offered independent
statistical mechanical explanations of black hole thermodynamics. But these
successes raise a new problem: why should models with such different
microscopic degrees of freedom yield identical results? I propose that the
asymptotic behavior of the density of states at a black hole horizon may be
determined by an underlying symmetry inherited from classical general
relativity, independent of the details of quantum gravity. I offer evidence
that a two-dimensional conformal symmetry at the horizon, with a classical
central extension, may provide the needed behavior.
