By employing random walk an analytic theory for the dissociation of singlet excitons in a random organic solid, for instance, a conjugated polymer, has been developed. At variance of conventional three-dimensional Onsager theory, it is assumed that an exciton with finite lifetime can first transfer endothermically an electron to an adjacent site, thereby generating a charge transfer state whose energy is above the energy of that of the initial exciton. In a second step the latter can fully dissociate in accordance with Onsager's concept Brownian motion. The results indicate that, depending of the energy required for the first jump, the first jump contributes significantly to the field dependence of the dissociation yield. Disorder weakens the temperature dependence of the yield dramatically and precludes extracting information on the exciton binding energy from it.