  We show that the asymptotic dynamics of three-dimensional gravity with
positive cosmological constant is described by Euclidean Liouville theory. This
provides an explicit example of a correspondence between de Sitter gravity and
conformal field theories. In the case at hand, this correspondence is
established by formulating Einstein gravity with positive cosmological constant
in three dimensions as an SL(2,C) Chern-Simons theory. The de Sitter boundary
conditions on the connection are divided into two parts. The first part reduces
the CS action to a nonchiral SL(2,C) WZNW model, whereas the second provides
the constraints for a further reduction to Liouville theory, which lives on the
past boundary of dS_3.
