In this Letter, using density functional theory based molecular dynamics simulations, we report that contact to a carbon nanotube (CNT) induces phase separation in an alloy catalyst, which promotes CNT growth. During growth of a CNT, the growth front tends to preferentially bond to the more active metal atom in the alloy catalyst, thus triggering a phase separation of the alloy catalyst particle. The accumulation of the active metal stabilizes the open end of the CNT, attracts carbon precursors to rapidly diffuse to the growth front, and avoids catalyst poisoning by preventing the encapsulation of the catalyst. This study resolves a long-term mystery surrounding the higher efficiency of alloy catalysts in CNT growth as compared to a pure metal catalyst and thereby paves the way to a more rational catalyst design for controlled CNT growth.