  We explore the formulation of non-rational 2D quantum gravity in terms of a
chiral CFT on a Riemann surface associated with the target space. The CFT in
question is constructed as the collective theory for a matrix chain, which is
dual to a statistical height model on dynamical triangulations. The heights are
associated with the sheets of the Riemann surface, which represents an infinite
branched cover of the spectral plane. We consider two examples of height
models: the SOS model and the semi-restricted SOS (SRSOS) model, in which the
heights are restricted from below. Both models are described in the continuum
limit by theories of 2D quantum gravity with conformal matter, perturbed by a
thermal operator (1,3). We give a compact operator expression for the n-loop
amplitudes as a collection of target space Feynman rules. The n-point functions
of local fields are obtained by shrinking the loops. In particular, we show
that the 4-point function of order operators in the SRSOS model coincides with
the 4-point function of the ``diagonal'' world sheet CFT studied in [1].
