  It is shown that conformal matter with $c_{\ssc L}\not=c_{\ssc R}$ can be
consistently coupled to two-dimensional `frame' gravity. The theory is
quantized, following David, and Distler and Kawai, using the derivation of
their {\it ansatz} due to Mavromatos and Miramontes, and D'Hoker and Kurzepa.
New super-selection rules are found by requiring SL(2,{\bf C}) invariance of
correlation functions on the plane. There is no analogue of the $c=1$ barrier
found in non-chiral non-critical strings. A non-critical heterotic string is
constructed---it has 744 states in its spectrum, transforming in the adjoint
representation of $(E_8)^3.$ Correlation functions are calculated in this
example.
