  We use complete enumeration and Monte Carlo techniques to study
two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$.
The interaction of charges at neighboring lattice sites is described by $q_i
q_j$. We find that a polymer undergoes a collapse transition at a temperature
$T_{\theta}$, which decreases with increasing imbalance between charges. At the
transition point, the dependence of the radius of gyration of the polymer on
the number of monomers is characterized by an exponent $\nu_{\theta} = 0.60 \pm
0.02$, which is slightly larger than the similar exponent for homopolymers. We
find no evidence of freezing at low temperatures.
