Separations represent a fundamental unit operation in biology and biotechnology. Commensurate with their importance is the diversity of methods that have been developed for performing them. One important class of separations are equilibrium gradient methods, wherein a medium with some type of spatial nonuniformity is combined with a force field to focus particles to equilibrium positions related to those particles' intrinsic properties. A second class of techniques that is nonequilibrium exploits labels to sort particles based upon their extrinsic properties. While equilibrium techniques such as iso-electric focusing (IEF) have become instrumental within analytical chemistry and proteomics, cell separations predominantly rely upon the second, label-based class of techniques, exemplified by fluorescence-activated cell sorting (FACS) and magnetic-activated cell sorting (MACS). To extend the equilibrium techniques available for separating cells, we demonstrate the first implementation of a new microfluidic equilibrium separation method, which we call isodielectric separation (IDS), for sorting cells based upon electrically distinguishable phenotypes. IDS is analogous to isoelectric focusing, except instead of separating amphoteric molecules in a pH gradient using electrophoresis, we separate cells and particles in an electrical conductivity gradient using dielectrophoresis. IDS leverages many of the advantages of microfluidics and equilibrium gradient separation methods to create a device that is continuous-flow, capable of parallel separations of multiple (>2) subpopulations from a heterogeneous background, and label-free. We demonstrate the separation of polystyrene beads based upon surface conductance as well as sorting nonviable from viable cells of the budding yeast Saccharomyces cerevisiae.