  The quantum mechanics of N slowly-moving charged BPS black holes in
five-dimensional ${\cal N}=1$ supergravity is considered. The moduli space
metric of the N black holes is derived and shown to admit 4 supersymmetries. A
near-horizon limit is found in which the dynamics of widely separated black
holes decouples from that of strongly-interacting, near-coincident black holes.
This decoupling suggests that the quantum states supported in the near-horizon
moduli space can be interpreted as internal states of a single composite black
hole carrying all of the charge. The near-horizon theory is shown to have an
enhanced D(2,1;0) superconformal symmetry. Eigenstates of the Hamiltonian H of
the near-horizon theory are ill-defined due to noncompact regions of the moduli
space corresponding to highly redshifted near-coincident black holes. It is
argued that one should consider, instead of H eigenstates, eigenstates of $2
L_0 = H+K$, where K is the generator of special conformal transformations. The
result is a well-defined Hilbert space with a discrete spectrum describing the
N-black hole dynamics.
