We report here the first synthesis of pure boron single-wall nanotubes by reaction of BCl3 with H-2 over an Mg-MCM-41 catalyst with parallel, uniform diameter (36 +/- 1Angstrom) cylindrical pores. The composition of the tubular structures observed in TEM was confirmed by electron energy loss spectroscopy, and the tubular geometry was confirmed by the presence of the characteristic spectral features in the Raman breathing mode region.