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We argue that the dominant charge carrier in glassy semiconducting alloys is a compound particle in the form of an electron or hole bound to an intimate pair of topological lattice defects; the particle is similar to the polaron solution of the Su–Schrieffer–Heeger Hamiltonian. The spatial component of the density of states for these special polarons is determined by the length scale of spatial modulation of electronegativity caused by a separate set of standalone topological defects. The latter length scale is fixed by the cooperativity size for structural relaxation; the size is largely independent of temperature in the glass but above melting, it decreases with temperature. Thus we predict that the temperature dependence of the electrical conductivity should exhibit a jump in the slope near the glass transition; the size of the jump is predicted to increase with the fragility of the melt. The predicted values of the jump and of the conductivity itself are consistent with experiment.