  We examine the question of finding the supersymmetric completion of the $R^4$
term in M-theory. Using superfield methods, we present an eight derivative
action in eight dimensions that has 32 preserved supersymmetries. We show also
that this action has a hidden eleven-dimensional Lorentz invariance. It can
thus be uplifted to give the complete set of bosonic terms in the M-theory
eight derivative action.
