  In this letter, we study the effects of weak off-diagonal disorder on
conjugated polymers with a doubly degenerate ground-state. We find that
disorder induces a finite density of neutral solitons in the lattice
dimerization of a polymer chain. Interchain interactions result in a linear
potential between the solitons and, if sufficiently strong, bind them into
pairs resulting in an exponential suppression of the soliton density. As
neutral solitons carry spin 1/2, they contribute to the polymer's magnetic
properties. We calculate the magnetic susceptibility and suggest measurements
of the magnetic susceptibility in {\it trans}-polyacetylene at low
temperatures.
