Carbon nanotubes in the form of multiwalled fullerenes are shown here to self-assemble under homogeneous gas-phase conditions of carbon condensation in an inert atmosphere heated to 1200 degrees C-conditions previously thought to be optimal only for the annealing and growth of C-60 and other spheroidal shells. Tubular fullerenes are known to be less stable than their spheroidal counterparts and have thus far been reported only in circumstances where some extrinsic factor (e.g., high electric fields, catalytic metal particles, hydrogen atoms, or a surface at low temperature) was available to help keep the fullerene structure open at its growing end. The experimental evidence reported here now indicates that multiwalled tube growth is inherent in the condensation of pure carbon vapors. Adatoms bonded between edge atoms of adjacent layers at the growing end are proposed to be the crucial intrinsic factor facilitating tube growth by stabilizing the open conformation against closure. This new view of the growing nanotube tip structure is likely to impact on nanotube growth mechanisms under other conditions, particularly the arc.