We present the first space- and time-resolved images of the spin-torque-induced steady-state oscillation of a magnetic vortex in a spin-valve nanostructure. We find that the vortex structure in a nanopillar is considerably more complicated than the 2D idealized structure often-assumed, which has important implications for the driving efficiency. The sense of the vortex gyration is uniquely determined by the vortex core polarity, confirming that the spin-torque acts as a source of negative damping even in such a strongly nonuniform magnetic system. The orbit radius is ∼10 nm, in agreement with micromagnetic simulations.