  We study the residual symmetry $SL(2,R)\otimes U(1)$ of the chiral gravity in
the light-cone gauge. Quantum gravitational effects renormalize the Kac-Moody
central charge and introduce, through the Lorentz anomaly, an arbitrary
parameter. Due to the presence of this free parameter the Kac-Moody central
charge has no forbidden range of values, and the strong gravity regime is open
to investigations.
