  We present a new quantization scheme for $2D$ gravity coupled to an $SU(2)$
principal chiral field and a dilaton; this model represents a slightly
simplified version of stationary axisymmetric quantum gravity. The analysis
makes use of the separation of variables found in our previous work [1] and is
based on a two-time hamiltonian approach. The quantum constraints are shown to
reduce to a pair of compatible first order equations, with the dilaton playing
the role of a ``clock field''. Exact solutions of the Wheeler-DeWitt equation
are constructed via the integral formula for solutions of the
Knizhnik-Zamolodchiokov equations.
