  Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limit
of Euclidean or complexified general relativity is not a free field theory, but
is a theory that describes a linearized self-dual connection propagating on an
arbitrary anti-self-dual background. This theory is quantized in the loop
representation and, as in the full theory, an infinite dimnensional space of
exact solutions to the constraint is found. An inner product is also proposed.
The path integral is constructed from the Hamiltonian theory and the measure is
explicitly computed nonperturbatively, without relying on a semiclassical
expansion. This theory could provide the starting point for a new approach to
perturbation theory in $G_{Newton}$ that does not rely on a background field
expansion and in which full diffeomorphism invariance is satisfied at each
order.
