Consistent two--dimensional chiral gravity

We study chiral induced gravity in the light-cone gauge and show that the theory is consistent for a particular choice of chiralities. The corresponding Kac--Moody central charge has no forbidden region of complex values. Generalized analysis of the critical exponents is given and their relation to the $SL(2,R)$ vacuum states is elucidated. All the parameters containing information about the theory can be traced back to the characteristics of the group of residual symmetry in the light--cone gauge.