  The main result of this paper is that the identity component of the
automorphism group of a compact, connected, strictly pseudoconvex CR manifold
is compact unless the manifold is CR equivalent to the standard sphere. In
dimensions greater than 3, it has been pointed out by D. Burns that this result
follows from known results on biholomorphism groups of complex manifolds with
boundary and the fact that any such CR manifold M can be realized as the
boundary of an analytic variety. When M is 3-dimensional, Burns's proof breaks
down because abstract CR 3-manifolds are generically not realizable as
boundaries. This paper provides an intrinsic proof of compactness that works in
any dimension.
