By an efficient algorithm, we evaluate exactly the disorder-averaged statis
tics of globally-neutral self-avoiding chains with quenched random charge q
(i)= +/-1 in monomer i and nearest neighbor interactions proportional to q(
i)q(j) on square (22 monomers) and cubic (16 monomers) lattices. At the The
ta transition in two dimensions, the radius of gyration and entropic and cr
ossover exponents are very compatible with the universality class of the co
rresponding transition of homopolymers. A further strong indication of such
a class comes from direct comparison with the corresponding annealed probl
em. In three dimensions, classical exponents are recovered. The percentage
of charge sequences leading to folding in a unique ground state approaches
zero exponentially with the chain length.