  This paper is concerned with the problem of coupling the N=8 superconformal
Bagger-Lambert-Gustavsson (BLG) theory to N=8 conformal supergravity in three
dimensions. We start by constructing the on-shell N=8 conformal supergravity in
three dimensions consisting of a Chern-Simons type term for each of the gauge
fields: the spin connection, the SO(8) R-symmetry gauge field and the spin 3/2
Rarita-Schwinger (gravitino) field. We then proceed to couple this theory to
the BLG theory. The final theory should have the same physical content, i.e.,
degrees of freedom, as the ordinary BLG theory. We discuss briefly the
properties of this "topologically gauged" BLG theory and why this theory may be
useful.
