A Fresnel lens is a chromatic, but low-loss optic, that can be used as a hard x-ray focusing element. In order to maintain phase coherence across the lens for a given x-ray wavelength, and to maximize transmission, material is deleted that removes multiples of 2 pi phase-shift. Using planar micro-electronics technology we have fabricated refractive Fresnel lenses for hard X-rays in single crystal silicon, and with the ideal shape.