The duality relating near-horizon microstates of black holes obtained as or
bifolds of a subset of AdS(3) to the states of a conformal field theory is
analyzed in detail. The SL(2; R)(L) X SL(2; R)(R) invariant vacuum on AdS(3
) corresponds to the NS-NS vacuum of the conformal field theory. The effect
of the orbifolding is to produce a density matrix, the temperature and ent
ropy of which coincide with the black hole. For string theory examples the
spectrum of chiral primaries agrees with the spectrum of multi-particle BPS
states for particle numbers less than of order the central charge. An uppe
r bound on the BPS particle number follows from the upper bound on the U(1)
charge of chiral primaries. This is a stringy exclusion principle which ca
nnot be seen in perturbation theory about AdS(3).