The successful synthesis of pure boron nitride (BN) nanotubes is reported here. Multi-walled tubes with inner diameters on the order of 1 to 3 nanometers and with lengths up to 200 nanometers were produced in a carbon-free plasma discharge between a BN-packed tungsten rod and a cooled copper electrode. Electron energy-loss spectroscopy on individual tubes yielded B:N ratios of approximately 1, which is consistent with theoretical predictions of stable BN tube structures.