Alternating exposures of nitrogen dioxide gas and trimethylaluminum vapor are shown to functionalize the surfaces of single-walled carbon nanotubes with a self-limited monolayer. Functionalized nanotube surfaces are susceptible to atomic layer deposition of continuous, radially isotropic material. This allows for the creation of coaxial nanotube structures of multiple materials with precisely controlled diameters. Functionalization involves only weak physical bonding, avoiding covalent modification, which should preserve the unique optical, electrical, and mechanical properties of the nanotubes.