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Virtual and augmented realities are rapidly developing technologies, but their large-scale penetration will require lightweight optical components with small aberrations. We demonstrate millimeter-scale diameter, high-NA, submicron-thin, metasurface-based lenses that achieve diffraction-limited achromatic focusing of the primary colors by exploiting constructive interference of light from multiple zones and dispersion engineering. To illustrate the potential of this approach, we demonstrate a virtual reality system based on a home-built fiber scanning near-eye display.