Black hole entropy from conformal symmetry on the horizon

The idea that black hole entropy might be governed by a conformal symmetry is an old one, but until now most efforts have focused on either asymptotic symmetries or symmetries on a ``stretched horizon.’’ For two-dimensional dilaton gravity, I show the existence of a well-behaved conformal symmetry that is \emph{on} the horizon, with a central charge that correctly determines the black hole entropy.