  Quantum gravity in 2+1 dimensions with a positive cosmological constant can
be represented as an SL(2,C) Chern-Simons gauge theory. The symmetric vacuum of
this theory is a degenerate configuration for which the gauge fields and
spacetime metric vanish, while de Sitter space corresponds to a highly excited
thermal state. Carlip's approach to black hole entropy can be adapted in this
context to determine the statistical entropy of de Sitter space. We find that
it equals one-quarter the area of the de Sitter horizon, in agreement with the
semiclassical formula.
