Ultra-small single-walled carbon nanotubes (SWNTs) are successfully fabricated in the channels of zeolite AlPO 4 -5 (AFI) single crystals by pyrolysis of tripropylamine molecules in the channels. These nanotubes have been observed directly by transmission electron microscopy, as well as by diffuse X-ray scattering and micro-Raman measurements of the nanotube breathing mode. The data consistently indicate a nanotube diameter of as small as 0.4nm, probably at or close to the theoretical limit. These mono-sized small nanotubes perhaps constitute the best example of one-dimensional (1-D) quantum wires. They show novel electronic properties. Investigation of the magnetic and transport properties of single-walled small diameter carbon nanotubes embedded in a zeolite matrix revealed that at temperatures below 20K, 0.4nm tubes exhibit superconducting behavior manifest as an anisotropic Meissner effect, with a superconducting gap and fluctuation super-current. The measured superconducting characteristics display smooth temperature variations owing to 1-D fluctuations, with a mean field superconducting transition temperature of 15K.