  In this paper we provide a possible realization of Penrose's idea of
nonlinear gravitons by constructing a solution to the initial value constraints
in Ashtekar variables. The solution inputs are a spatial SU(2) connection and
two free functions of position, and can be constructed as a formal operatorial
expansion in powers of the cosmological constant about spacetimes of Petrov
Type O. We first present the linear case, and then provide a simple nonlinear
example to first order using a spatially homogeneous connection.
