The exact formula derived by us earlier for the entropy of a four dimension
al nonrotating black hole within the quantum geometry formulation of the ev
ent horizon in terms of boundary states of a three dimensional Chern-Simons
theory is reexamined for large horizon areas. In addition to the semiclass
ical Bekenstein-Hawking contribution proportional to the area obtained earl
ier, we find a contribution proportional to the logarithm of the area toget
her with subleading corrections that constitute a series in inverse powers
of the area.