Chirality-controlled synthesis of single-wall carbon nanotubes with predefined chiralities has been an important but elusive goal for almost two decades. Here we demonstrate a general strategy for producing carbon nanotubes with predefined chiralities by using purified singlechirality nanotubes as seeds for subsequent metal catalyst free growth, resembling vapourphase epitaxy commonly used for semiconductor films. In particular, we have successfully synthesized (7, 6), (6, 5) and (7, 7) nanotubes, and used Raman spectroscopy to show unambiguously that the original chiralities of the nanotube seeds are preserved. Furthermore, we have performed electrical measurements on synthesized individual (7, 6) and (6, 5) nanotubes, confirming their semiconducting nature. The vapour-phase epitaxy approach is found to be highly robust and should enable a wide range of fundamental studies and technological developments.