The synthesis of carbon nanotubes (CNTs) of desired chiralities and diameters is one of the most important challenges in nanotube science and achieving such selectivity may require a detailed understanding of their growth mechanism. We report the formation of CNTs in an entirely condensed phase process that allows us, for the first time, to monitor the nucleation of a nanotube on the spherical surface of a metal particle. When multiwalled CNTs containing metal particle cores are irradiated with an electron beam, carbon from graphitic shells surrounding the metal particles is ingested into the body of the particle and subsequently emerges as single-walled nanotubes (SWNTs) or multiwalled nanotubes (MWNTs) inside the host nanotubes. These observations, at atomic resolution in an electron microscope, show that there is direct bonding between the tubes and the metal surface from which the tubes sprout and can be readily explained by bulk diffusion of carbon through the body of catalytic particles, with no evidence of surface diffusion.