  We argue that classical $(\alpha')$ effects qualitatively modify the
structure of Euclidean black hole horizons in string theory. While low energy
modes experience the geometry familiar from general relativity, high energy
ones see a rather different geometry, in which the Euclidean horizon can be
penetrated by an amount that grows with the radial momentum of the probe. We
discuss this in the exactly solvable SL(2,R)/U(1) black hole, where it is a
manifestation of the black hole/Sine-Liouville duality.
