We use real-time observations of the growth of copper-catalyzed silicon nanowires to determine the nanowire growth mechanism directly and to quantify the growth kinetics of individual wires. Nanowires were grown in a transmission electron microscope using chemical vapor deposition on a copper-coated Si substrate. We show that the initial reaction is the formation of a silicide, eta'-Cu(3)Si, and that this solid silicide remains on the wire tips during growth so that growth is by the vapor-solid-solid mechanism. Individual wire directions and growth rates are related to the details of orientation relation and catalyst shape, leading to a rich morphology compared to vapor-liquid-solid grown nanowires. Furthermore, growth occurs by ledge propagation at the silicide/silicon interface, and the ledge propagation kinetics suggest that the solubility of precursor atoms in the catalyst is small, which is relevant to the fabrication of abrupt heterojunctions in nanowires.