In its formulation as a Chern-Simons theory, three-dimensional general relativity induces a Wess-Zumino-Witten action on spatial boundaries. Treating the horizon of the three-dimensional Euclidean black hole as a boundary, I count the states of the resulting WZW model, and show that when analytically continued back to Lorentzian signature, they yield the correct Bekenstein-Hawking entropy. The relevant states can be understood as "would-be gauge" degrees of freedom that become dynamical at the horizon.