We demonstrate the continued growth of single-walled carbon nanotubes (SWNTs) from ordered arrays of open-ended SWNTs in a way analogous to epitaxy. Nanometer-sized metal catalysts were docked to the SWNT open ends and subsequently activated to restart growth. SWNTs thus grown inherit the diameters and chirality from the seeded SWNTs, as indicated by the closely matched frequencies of Raman radial breathing modes before and after the growth.