Linear defects are generic in continuous media(1). In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum field theories they are known as cosmic strings(2), in superconductors as quantized flux lines(3), and in superfluids(3,4) and low-density Bose-Einstein condensates(5) as quantized vortex lines. A conventional quantized vortex Line consists of a central core around which the phase of the order parameter winds by 2 pi n, while within the core the order parameter vanishes or is depleted from the bulk value. Usually vortices are singly quantized (that is, have n = 1). But it has been theoretically predicted that, in superfluid He-3-A, vortex lines are possible that have n = 2 and continuous structure, so that the orientation of the multicomponent order parameter changes smoothly throughout the vortex while the amplitude remains constant. Here we report direct proof, based on high-resolution nuclear magnetic resonance measurements, that the most common vortex line in He-3-A has n = 2. One vortex line after another is observed to form in a regular periodic process, similar to a phase-slip in the Josephson effect.