  Black holes in 2+1 dimensions enjoy long range topological interactions
similar to those of non-abelian anyon excitations in a topologically ordered
medium. Using this observation, we compute the topological entanglement entropy
of BTZ black holes, via the established formula S_top = log(S^a_0), with S_b^a
the modular S-matrix of the Virasoro characters chi_a(tau). We find a precise
match with the Bekenstein-Hawking entropy. This result adds a new twist to the
relationship between quantum entanglement and the interior geometry of black
holes. We generalize our result to higher spin black holes, and again find a
detailed match. We comment on a possible alternative interpretation of our
result in terms of boundary entropy.
