  We study CR geometry in arbitrary codimension, and introduce a process, which
we call the Levi-Kahler quotient, for constructing Kahler metrics from CR
structures with a transverse torus action. Most of the paper is devoted to the
study of Levi-Kahler quotients of toric CR manifolds, and in particular,
products of odd dimensional spheres. We obtain explicit descriptions and
characterizations of such quotients, and find Levi-Kahler quotients of products
of 3-spheres which are extremal in a weighted sense introduced by G. Maschler
and the first author.
