Legged robots can sustain stable dynamic locomotion without sensors or feedback. It is possible to construct a running robot that is inherently stable and needs no sensing to reject minor perturbations; it is therefore self-stabilizing. In contrast, most previous attempts to make robots run have used active, high bandwidth feedback control systems. We use a simplified monopod to give an understandable reason why self-stabilizing running should be possible. Physically realistic simulations running with one, two, or four legs demonstrate self-stabilizing running, as does a physical monopod robot.