Chiral (N=1) supergravity

We consider a purely imaginary translational Chern-Simons term, evaluated by using the Cartan relation between torsion and spin. By means of the introduction of this term as a boundary term, a chiral reformulation of (N = 1) supergravity is achieved. The translational Chern-Simons term plays the role of a generating function for the canonical transformation, which splits the supergravity field variables into self-dual and anti-self-dual parts in a natural way.