  We formulate topologically massive supergravity with cosmological constant in
the first order formalism, and construct the Noether supercurrent and
superpotential associated with its local supersymmetry. Using these results, we
construct in ordinary topologically massive gravity the Witten-Nester integral
for conserved charges containing spinors which satisfy a generalized version of
Witten equation on the initial value surface. We show that the Witten-Nester
charge, represented as an integral over the boundary of the initial value
surface produces the Abbott-Deser-Tekin energy for asymptotically anti de
Sitter spacetimes. We consider all values of the Chern-Simons coupling
constant, including the critical value known as the chiral point, and study the
cases of standard Brown-Henneaux boundary conditions, as well as their weaker
version that allow a slower fall-off. Studying the Witten-Nester energy as a
bulk integral over the initial value surface instead, we find a bound on the
energy, and through it the sufficient condition for the positivity of the
energy. In particular, we find that spacetimes of Petrov type N that admit
globally well defined solutions of the generalized Witten equation have
positive energy.
