We demonstrate single nanowire tunnel diodes with room temperature peak current densities of up to 329 A/cm(2). Despite the large surface to volume ratio of the type-II InP-GaAs axial heterostructure nanowires, we measure peak to valley current ratios (PVCR) of up to 8.2 at room temperature and 27.6 at liquid helium temperature. These sub-100-nm-diameter structures are promising components for solar cells as well as electronic applications.