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 g
eometry, 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.
