  We compute the tree-level scattering amplitude between two covariantly
conserved sources in generic Cosmological Topologically Massive Gravity
augmented with a Fierz-Pauli term that has three massive degrees of freedom. We
consider the Chiral Gravity limit in the anti-de Sitter space as well as the
limit of Flat-Space Chiral Gravity. We show that Chiral Gravity cannot be
unitarily deformed with a Fierz-Pauli mass. We calculate the non-relativistic
potential energy between two point-like spinning sources. In addition to the
expected mass-mass and spin-spin interactions, there are mass-spin interactions
due to the presence of the gravitational Chern-Simons term which induces spin
for any massive object and turns it to an anyon. We also show that the
tree-level scattering is trivial for the Flat-Space Chiral Gravity.
