The quantum statistics of charged, extremal black holes is investigated beginning with the hypothesis that the quantum state is a functional on the space of closed three-geometries, with each black hole connected to an oppositely charged black hole through a spatial wormhole. From this starting point a simple argument is given that a collection of extremal black holes obeys neither Bose nor Fermi statistics. Rather they obey an exotic variety of particle statistics known as ``infinite statistics'' which resembles that of distinguishable particles and is realized by a $q$-deformation of the quantum commutation relations.

12 pages