  A `black hole sector' of non-perturbative canonical quantum gravity is
introduced. The quantum black hole degrees of freedom are shown to be described
by a Chern-Simons field theory on the horizon. It is shown that the entropy of
a large non-rotating black hole is proportional to its horizon area. The
constant of proportionality depends upon the Immirzi parameter, which fixes the
spectrum of the area operator in loop quantum gravity; an appropriate choice of
this parameter gives the Bekenstein-Hawking formula S = A/4*l_p^2. With the
same choice of the Immirzi parameter, this result also holds for black holes
carrying electric or dilatonic charge, which are not necessarily near extremal.
