  The non-minimal coupling of a scalar field is considered in the framework of
Ashtekar's new variables formulation of gravity. A first order action
functional for this system is derived in which the field variables are a tetrad
field, and an SL(2,C) connection, together with the scalar field. The tetrad
field and the SL(2,C) connection are related to the Ashtekar variables for the
vacuum case by a conformal transformation. A canonical analysis shows that for
this coupling the equations of Ashtekar's formulation of canonical gravity are
non-polynomial in the scalar field. (to be published in Phys. Rev. D)
