In lithium-ion batteries, the electrochemical reaction between the electrodes and lithium is a critical process that controls the capacity, cyclability and reliability of the battery. Despite intensive study, the atomistic mechanism of the electrochemical reactions occurring in these solid-state electrodes remains unclear. Here, we show that in situ transmission electron microscopy can be used to study the dynamic lithiation process of single-crystal silicon with atomic resolution. We observe a sharp interface (~1 nm thick) between the crystalline silicon and an amorphous Li(x)Si alloy. The lithiation kinetics are controlled by the migration of the interface, which occurs through a ledge mechanism involving the lateral movement of ledges on the close-packed {111} atomic planes. Such ledge flow processes produce the amorphous Li(x)Si alloy through layer-by-layer peeling of the {111} atomic facets, resulting in the orientation-dependent mobility of the interfaces.