Three dimensional Einstein gravity with negative cosmological constant -1/ell^2 deformed by a gravitational Chern-Simons action with coefficient 1/mu is studied in an asymptotically AdS_3 spacetime. It is argued to violate unitary or positivity for generic mu due to negative-energy massive gravitons. However at the critical value muell=1, the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by ell M=J. The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges (c_L,c_R)=(0,3ell /G).
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