Since 1942, when Arthur Rosinger and Edward McLaughlin invented the magnetic stirrer, it has been known that if the submerged stirring bar-magnet is driven too quickly it will hop erratically on the base of the container, earning it the nickname ‘the flea’. We find that if the viscosity of the liquid is high enough, the flea instead jumps up and levitates indefinitely, bouncing up and down, waggling backwards and forwards while slowly rotating -- and not stirring the solution at all. We discover that the back-and-forth motion pumps fluid out to the sides, and stabilizes the flea. Intriguingly, if the viscosity is slowly reduced, the flow direction reverses, and the flea falls. This discovery should motivate the design of bi-directional fluidic pumps, improve understanding of effective swimming methods, and provide a new levitation route for container-less storage or friction-less transport.