Investigations of swimming at low Reynolds numbers (Re < 10(-4)) so far have focused on individual or collectively moving autonomous microswimmers consisting of a single active building unit. Here we show that linear propulsion can also be reproducibly generated in a self-assembled dynamic complex formed from a granular, HCl-releasing particle settled on a charged quartz wall and a swarm of micrometer-sized negatively charged colloids. In isolation, none of the constituents shows motion beyond diffusion. When brought together, they self-assemble into a complex capable of directed swimming. It is stabilized by toroidal solvent flow centered about the granular particle. Propulsion is then launched by an asymmetric distribution of the colloids. Motion is self-stabilizing and continues for up to 25 min with velocities of 1-3 mu m/s. Although the details of the mechanisms involved pose a formidable experimental and theoretical challenge, our observations offer a conceptually new, well-reproduced, versatile approach to swimming and transport at low Reynolds numbers.