Carbon nanotubes have been regarded since their discovery(1) as potential molecular quantum wires. In the case of multi-wall nanotubes, where many tubes are arranged in a coaxial fashion, the electrical properties of individual tubes have been shown to vary strongly from tube to tube(2,3), and to be characterized by disorder and localization(4). Single-wall nanotubes(5,6) (SWNTs) have recently been obtained with high yields and structural uniformity(7). Particular varieties of these highly symmetric structures have been predicted to be metallic, with electrical conduction occurring through only two electronic modes(8-10). Because of the structural symmetry and stiffness of SWNTs, their molecular wavefunctions may extend over the entire tube. Here we report electrical transport measurements on individual single-wall nanotubes that confirm these theoretical predictions. We find that SWNTs indeed act as genuine quantum wires, Electrical conduction seems to occur through well separated, discrete electron states that are quantum-mechanically coherent over long distance, that is at least from contact to contact (140 nm), Data in a magnetic field indicate shifting of these,states due to the Zeeman effect.