  A Lagrangian description of a maximally supersymmetric conformal field theory
in three dimensions was constructed recently by Bagger and Lambert (BL). The BL
theory has SO(4) gauge symmetry and contains scalar and spinor fields that
transform as 4-vectors. We verify that this theory has OSp(8|4) superconformal
symmetry and that it is parity conserving despite the fact that it contains a
Chern--Simons term. We describe several unsuccessful attempts to construct
theories of this type for other gauge groups and representations. This
experience leads us to conjecture the uniqueness of the BL theory. Given its
large symmetry, we expect this theory to play a significant role in the future
development of string theory and M-theory.
