The growth of populations is known to be influenced by dispersal, which has often been described as purely diffusive. In the open ocean, however, the tendrils and filaments of phytoplankton populations provide evidence for dispersal by stirring. Despite the apparent importance of horizontal stirring for plankton ecology, this process remains poorly characterized. Here we investigate the development of a discrete phytoplankton bloom, which was initiated by the iron fertilization of a patch of water (7 km in diameter) in the Southern Ocean. Satellite images show a striking, 150-km-long bloom near the experimental site, six weeks after the initial fertilization. We argue that the ribbon-like bloom was produced from the fertilized patch through stirring, growth and diffusion, and we derive an estimate of the stirring rate. In this case, stirring acts as an important control on bloom development, mixing phytoplankton and iron out of the patch, but also entraining silicate. This may have prevented the onset of silicate limitation, and so allowed the bloom to continue for as long as there was sufficient iron. Stirring in the ocean is likely to be variable, so blooms that are initially similar may develop very differently.