The conduction properties of ClC-0 and ClC-1 chloride channels are examined using electrostatic calculations and three-dimensional Brownian dynamics simulations. We create an open-state configuration of the prokaryotic ClC Cl- channel using its known crystallographic structure as a basis. Two residues that are occluding the channel are slowly pushed outward with molecular dynamics to create a continuous ion-conducting path with the minimum radius of 2.5 Angstrom. Then, retaining the same pore shape, the prokaryotic ClC channel is converted to either ClC-0 or ClC-1 by replacing all the nonconserved dipole-containing and charged amino acid residues. Employing open-state ClC-0 and ClC-1 channel models, current-voltage curves consistent with experimental measurements are obtained. We find that conduction in these pores involves three ions. We locate the binding sites, as well as pinpointing the rate-limiting steps in conduction, and make testable predictions about how the single channel current across ClC-0 and ClC-1 will vary as the ionic concentrations are increased. Finally, we demonstrate that a ClC-0 homology model created from an alternative sequence alignment fails to replicate any of the experimental observations.