  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.
