  Thomas-Whitehead (TW) gravity was recently introduced as a projective gauge
theory of gravity over a d-dimensional manifold that embeds reparameterization
invariance into the action functional for gravitation through the use of the
Thomas-Whitehead connection. The projective invariance in this d-dimensional
theory enjoys an intimate relationship with the Virasoro coadjoint elements
found in string theory as one of the components of the connection,
$\mathcal{D}_{ab}$, is directly related to the coadjoint elements of the
Virasoro algebra. TW Gravity exploits projective Gauss-Bonnet terms in the
action functional which allows the theory to collapse to Einstein's theory of
General Relativity in the limit that $\mathcal{D}_{ab }$ vanishes. In this note
we develop the graded extension of TW Gravity, Super TW Gravity, in the
framework of a DeWitt supermanifold. We construct the Lagrangian for Super TW
Gravity, give a detailed derivation of the classical field equations and
discuss the graded extension of the projective connection as a prelude to a
future understanding of TW-Supergravity (which has manifest supersymmetry) and
its relationship to the Super-Virasoro algebra.
