While the Marangoni-stress-driven spreading of surfactants along continuous fluid interfaces is a well-studied problem, we demonstrate experimentally that swift and efficient surfactant transport can also occur along discontinuous interfaces. We used chemical surface patterning to create arrays of discrete drops and liquid bridges immersed inside a second immiscible liquid. Surface-active compounds introduced at one end of the linear array are transported along the array via surfactant-induced interfacial convection at a rate by far exceeding diffusion. We believe this mechanism to be relevant to the application of surfactants in enhanced oil recovery, where oil-water interfaces are likely to be discontinuous. Marangoni flows can provide access to dead-end pores and low-permeability regions that are otherwise bypassed by conventional pressure-driven waterfloods.