The density matrix formalism is used to consider long-range electron transfer through a delocalized bridge system that is dissipatively coupled to a thermal bath. Under conditions when the bridge is weakly populated, a distance-independent transfer mechanism arises that eventually dominates the exponentially distance-dependent nonadiabatic tunneling process typically observed. This model offers a possible explanation for the anomalously rapid long-range photoelectron transfer recently observed by Barton and Turro et al. for donor and acceptor species intercalated into a DNA double helix (Science 1993, 262, 1025). Predicted electron-transfer rates are obtained by numerically solving the Redfield equation for the density matrix of the full donor-bridge-acceptor system in the presence of stochastic fluctuations induced by the bath.