We exploit the inherent dispersion in diffractive optics to demonstrate planar chromatic-aberration-corrected lenses. Specifically, we designed, fabricated and characterized cylindrical diffractive lenses that efficiently focus the entire visible band (450 nm to 700 nm) onto a single line. These devices are essentially pixelated, multi-level microstructures. Experiments confirm an average optical efficiency of 25% for a three-wavelength apochromatic lens whose chromatic focus shift is only 1.3 μm and 25 μm in the lateral and axial directions, respectively. Super-achromatic performance over the continuous visible band is also demonstrated with averaged lateral and axial focus shifts of only 1.65 μm and 73.6 μm, respectively. These lenses are easy to fabricate using single-step grayscale lithography and can be inexpensively replicated. Furthermore, these devices are thin (<3 μm), error tolerant, has low aspect ratio (<1:1) and offer polarization-insensitive focusing, all significant advantages compared to alternatives that rely on metasurfaces. Our design methodology offers high design flexibility in numerical aperture and focal length, and is readily extended to 2D.