The qualitative behavior of charged particles in a vacuum is given by Earnshaw's theorem, which states that there is no steady configuration of charged particles in a vacuum that is asymptotically stable to perturbations. In a viscous fluid, examples of stationary configurations of sedimenting uncharged particles are known, but they are unstable or neutrally stable-they are not attractors. In this Letter, it is shown by example that two charged particles settling in a fluid may have a configuration that is asymptotically stable to perturbations for a wide range of charges, radii, and densities. The existence of such "bound states" is essential from a fundamental point of view and it can be significant for dilute charged particulate systems in various biological, medical, and industrial contexts.