  We show that the Bagger-Lambert theory of multiple M2-branes fits into the
general construction of maximally supersymmetric gauge theories using the
embedding tensor technique. We apply the embedding tensor technique in order to
systematically obtain the consistent gaugings of N=8 superconformal theories in
2+1 dimensions. This leads to the Bagger-Lambert theory, with the embedding
tensor playing the role of the four-index antisymmetric tensor defining a
``3-algebra''. We present an alternative formulation of the theory in which the
embedding tensor is replaced by a set of unrestricted scalar fields. By taking
these scalar fields to be parity-odd, the Chern-Simons term can be made
parity-invariant.
