  In the metric formulation gravitons are described with the parity symmetric
$S_+^2\otimes S_-^2$ representation of Lorentz group. General Relativity is
then the unique theory of interacting gravitons with second order field
equations. We show that if a chiral $S_+^3\otimes S_-$ representation is used
instead, the uniqueness is lost, and there is an infinite-parametric family of
theories of interacting gravitons with second order field equations. We use the
language of graviton scattering amplitudes, and show how the uniqueness of GR
is avoided using simple dimensional analysis. The resulting distinct from GR
gravity theories are all parity asymmetric, but share the GR MHV amplitudes.
They have new all same helicity graviton scattering amplitudes at every
graviton order. The amplitudes with at least one graviton of opposite helicity
continue to be determinable by the BCFW recursion.
