  Black holes in equilibrium can be defined locally in terms of the so-called
isolated horizon boundary condition given on a null surface representing the
event horizon. We show that this boundary condition can be treated in a
manifestly SU(2) invariant manner. Upon quantization, state counting is
expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere
with marked points. Moreover, the counting can be mapped to counting the number
of SU(2) intertwiners compatible with the spins that label the defects. The
resulting BH entropy is proportional to a_H with logarithmic corrections \Delta
S=-3/2 \log a_H. Our treatment from first principles completely settles
previous controversies concerning the counting of states.
