Several cell lineages migrate through the developing and adult tissues of our bodies utilising a variety of modes of motility to suit the different substrates and environments they encounter en route to their destinations. Here we describe a novel adhesion-independent mode of single cell locomotion utilised by Drosophila fat body cells - the equivalent of vertebrate adipocytes. Like their human counterpart, these large cells were previously presumed to be immotile. However, in the Drosophila pupa fat body cells appear to be motile and migrate in a directed way towards wounds by peristaltic swimming through the hemolymph. The propulsive force is generated from a wave of cortical actomyosin that travels rearwards along the length of the cell. We discuss how this swimming mode of motility overcomes the physical constraints of microscopic objects moving in fluids, how fat body cells switch on other "motility machinery" to plug the wound on arrival, and whether other cell lineages in Drosophila and other organisms may, under certain circumstances, also adopt swimming as an effective mode of migration.