Investigation of the magnetic and transport properties of single-walled small-diameter carbon nanotubes embedded in a zeolite matrix revealed that at temperatures below 20 kelvin, 4 angstrom tubes exhibit superconducting behavior manifest as an anisotropic Meissner effect, with a superconducting gap and fluctuation supercurrent. The measured superconducting characteristics display smooth temperature variations owing to one-dimensional fluctuations, with a mean-field superconducting transition temperature of 15 kelvin. Statistical mechanic calculations based on the Ginzburg-Landau free-energy functional yield predictions that are in excellent agreement with the experiments.