  Parity (P) violation in gravity would be a sure sign of new physics. We
examine the possibility of P violation in the cosmological redshift. If right-
and left-circularly polarized photons experience the redshift differently, the
radiation from distant sources would tend to be depolarized, since the
polarizations states would accumulate different phases during propagation. The
resulting birefringence has an unusual signature--depending on z^2--quite
unlike what is seen in other theories, including those with violation of local
boost invariance. The observed broad-spectrum polarization of $\gamma$-ray
bursts constrains the fractional difference between the right- and left-handed
redshifts at the 6 x 10^(-37) level.
