  A new matrix model is described, based on the exceptional Jordan algebra. The
action is cubic, as in matrix Chern-Simons theory. We describe a
compactification that, we argue, reproduces, at the one loop level, an
octonionic compactification of the matrix string theory in which SO(8) is
broken to G2. There are 27 matrix degrees of freedom, which under Spin(8)
transform as the vector, spinor and conjugate spinor, plus three singlets,
which represent the two longitudinal coordinates plus an eleventh coordinate.
Supersymmetry appears to be related to triality of the representations of
Spin(8).
