  We examine a Chern-Simons matrix model which we propose as a toy model for
studying the quantum nature of black holes in 2+1 gravity. Its dynamics is
described by two $N\times N$ matrices, representing the two spatial
coordinates. The model possesses an internal SU(N) gauge symmetry, as well as
an external rotation symmetry. The latter corresponds to the rotational
isometry of the BTZ solution, and does not decouple from SU(N) gauge
transformations. The system contains an invariant which is quadratic in the
spatial coordinates. We obtain its spectrum and degeneracy, and find that the
degeneracy grows exponentially in the large $N$ limit. The usual BTZ black hole
entropy formula is recovered upon identifying the quadratic invariant with the
square of the black hole horizon radius. The quantum system behaves
collectively as an integer (half-integer) spin particle for even (odd) $N$
under $2\pi$-rotations.
