  We focus on N = 3 chiral supergravity (SUGRA) which is the lowest N theory
involving a spin-1/2 field, and derive the Ashtekar's canonical formulation of
N = 3 SUGRA starting with the chiral Lagrangian constructed by closely
following the standard SUGRA. The polynomiality of constraints in terms of
canonical variables and the graded algebraic structure of constraints are
discussed in the canonical formulation. In particular, we show the
polynomiality of the {\it rescaled} right- and left-handed SUSY constraints by
a nonpolynomial factor. And also we show the graded algebraic structure of
Osp(3/2) in the constraint algebra by calculating the Poisson brackets of
Gauss, SU(2) gauge and right-handed SUSY constraints, although the algebra
among only those three types of constraints does not closed.
