  A polymer folding model on the square lattice is constructed with attractive
contact interactions of strength 1/c^2, 0<c<1. The corresponding model on a
dynamical random lattice, with freely fluctuating co-ordination number at each
vertex, is formulated as a random two-matrix model and an expression for the
partition function of a length-L chain is derived. Numerical estimates and
analytical evaluation for L \to \infty shows a third-order collapse transition
at c=\sqrt{2}-1. Geometrical critical exponents are computed in each phase and
interpreted. The Knizhnik-Polyakov-Zamolodchikov 2D quantum gravity scaling
relations are used to predict the corresponding behaviour on the regular
lattice, which lies in a different universality class from the percolation
Theta-point of Duplantier and Saleur.
