  Liouville theory is shown to describe the asymptotic dynamics of
three-dimensional Einstein gravity with a negative cosmological constant. This
is because (i) Chern-Simons theory with a gauge group $SL(2,R) \times SL(2,R)$
on a space-time with a cylindrical boundary is equivalent to the non-chiral
$SL(2,R)$ WZW model; and (ii) the anti-de Sitter boundary conditions implement
the constraints that reduce the WZW model to the Liouville theory.
