  A set of new canonical variables for $d=11$ supergravity is proposed which
renders the supersymmetry variations and the supersymmetry constraint
polynomial. The construction is based on the $SO(1,2)\times SO(16)$ invariant
reformulation of $d=11$ supergravity given in previous work, and has some
similarities with Ashtekar's reformulation of Einstein's theory. The new
bosonic variables fuse the gravitational degrees of freedom with those of the
three-index photon $A_{MNP}$ in accordance with the hidden symmetries of the
dimensionally reduced theory. Although $E_8$ is not a symmetry of the theory,
the bosonic sector exhibits a remarkable $E_8$ structure, hinting at the
existence of a novel type of ``exceptional geometry''.
