  To write down a path integral for the Ashtekar gravity one must solve three
fundamental problems. First, one must understand rules of complex contour
functional integration with holomorphic action. Second, one should find which
gauges are compatible with reality conditions. Third, one should evaluate the
Faddeev-Popov determinant produced by these conditions. In the present paper we
derive the BRST path integral for the Hilbert-Palatini gravity. We show, that
for certain class of gauge conditions this path integral can be re-written in
terms of the Ashtekar variables. Reality conditions define contours of
integration. For our class of gauges all ghost terms coincide with what one
could write naively just ignoring any Jacobian factors arising from the reality
conditions.
