  We show how the recently introduced "Pure Connection Formulation" of gravity
provides a natural framework for approaching the problem of computing graviton
scattering amplitudes. In particular, we show that the interaction vertices are
greatly simplified in this formalism as compared to the Einstein-Hilbert
perturbation theory. This, in turns, leads to very simple Feynman rules that we
employ for the direct computations. Furthermore, this framework naturally
extends to wider class of gravitational theories, which encompasses General
Relativity as a special case. We compute all the possible tree-level
graviton-graviton scattering amplitudes for a general theory from this class.
In the GR case the results are in complete accordance with the known
expressions in the literature. Moreover, for the general theory distinct from
GR, we find new tree-level parity-violating amplitudes. The presence of this
new amplitudes is a direct consequence of the fact that the general theory does
not exhibit explicit parity invariance.
