The diffusion induced migration of a wall of edge dislocations is considered. The dislocations are assumed to be fast diffusion pipes, connected at their ends to solute sinks, and in equilibrium with these sinks along their lengths. We find that the array of edge dislocations is stabilized by the long range solute stress field (a solute misfit is necessary), and is capable of synchronous climb in response to local solute stress fields. The climb of the dislocation wall acts to channel solute to the sinks, in close analogy with chemically induced grain boundary migration. Expressions are derived for the climb force on a single dislocation, and on the dislocations in the wall. The stability of the migrating wall as a function of dislocation spacing and velocity is discussed.