Chemical vapour deposition of two-dimensional materials typically involves the conversion of vapour precursors to solid products in a vapour-solid-solid mode. Here, we report the vapour-liquid-solid growth of monolayer MoS2, yielding highly crystalline ribbons with a width of few tens to thousands of nanometres. This vapour-liquid-solid growth is triggered by the reaction between MoO3 and NaCl, which results in the formation of molten Na-Mo-O droplets. These droplets mediate the growth of MoS2 ribbons in the 'crawling mode' when saturated with sulfur. The locally well-defined orientations of the ribbons reveal the regular horizontal motion of the droplets during growth. Using atomic-resolution scanning transmission electron microscopy and second harmonic generation microscopy, we show that the ribbons are grown homoepitaxially on monolayer MoS2 with predominantly 2H- or 3R-type stacking. Our findings highlight the prospects for the controlled growth of atomically thin nanostructure arrays for nanoelectronic devices and the development of unique mixed-dimensional structures.