  The superradiant scattering of a scalar field with frequency and angular
momentum (\omega,m) by a near-extreme Kerr black hole with mass and spin (M,J)
was derived in the seventies by Starobinsky, Churilov, Press and Teukolsky. In
this paper we show that for frequencies scaled to the superradiant bound the
full functional dependence on (\omega,m,M,J) of the scattering amplitudes is
precisely reproduced by a dual two-dimensional conformal field theory in which
the black hole corresponds to a specific thermal state and the scalar field to
a specific operator. This striking agreement corroborates a conjectured
Kerr/CFT correspondence.
