  We study Chern-Simons theory with a complex G_C or a real G x G gauge group
on a manifold with boundary - this includes Lorentzian and Euclidean (anti-) de
Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a
canonical choice of boundary conditions that leads to an unambiguous, fully
covariant and gauge invariant, off-shell derivation of the boundary action - a
G_C/G or G WZW model, coupled in a gauge invariant way to the boundary value of
the gauge field. In particular, for (E/A)dS gravity, the boundary action is a
WZW model with target space (E/A)dS_3, reminiscent of a worldsheet for
worldsheet mechanism. We discuss in some detail the properties of the boundary
theories that arise and we confront our results with various related
constructions in the literature.
