Abstract
Three dimensional Einstein gravity with negative cosmological constant
-1/\ell^2 deformed by a gravitational Chern-Simons action with coefficient
1/is studied in an asymptotically AdS\_3 spacetime. It is argued to violate
unitary or positivity for generic due to negative-energy massive gravitons.
However at the critical value \mu\ell=1, the massive gravitons disappear and
BTZ black holes all have mass and angular momentum related by 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)=(0,3/G).
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