We fabricate and characterize a metal-dielectric nanostructure with an effective refractive index n=0 in the visible spectral range. Light is excited in the material at deep subwavelength resolution by a 30-keV electron beam. From the measured spatially and angle-resolved emission patterns, a vanishing phase advance, corresponding to an effective ϵ=0 and n=0, is directly observed at the cutoff frequency. The wavelength at which this condition is observed can be tuned over the entire visible or near-infrared spectral range by varying the waveguide width. This n=0 plasmonic nanostructure may serve as a new building block in nanoscale optical integrated circuits and to control spontaneous emission as experimentally demonstrated by the strongly enhanced radiative optical density of states over the entire n=0 structure.