Numerous natural systems contain surfaces or threads that enable directional water transport1–7. This behaviour is usually ascribed to hierarchical structural features at the microscale and nanoscale, with gradients in surface energy8,9 and gradients in Laplace pressure10 thought to be the main driving forces. Here we study the prey-trapping pitcher organs of the carnivorous plant Nepenthes alata. We find that continuous, directional water transport occurs on the surface of the ‘peristome’—the rim of the pitcher—because of its multiscale structure, which optimizes and enhances capillary rise11,12 in the transport direction, and prevents backflow by pinning in place any water front that is moving in the reverse direction. This results not only in unidirectional flow despite the absence of any surface-energy gradient, but also in a transport speed that is much higher than previously thought. We anticipate that the basic ‘design’ principles underlying this behaviour could be used to develop artificial fluid-transport systems with practical applications.