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Microwave Kinetic Inductance Detectors, or MKIDs, have proven to be a powerful cryogenic detector technology due to their sensitivity and the ease with which they can be multiplexed into large arrays. A MKID is an energy sensor based on a photon-variable superconducting inductance in a lithographed microresonator, and is capable of functioning as a photon detector across the electromagnetic spectrum as well as a particle detector. Here we describe the first successful effort to create a photon-counting, energy-resolving ultraviolet, optical, and near infrared MKID focal plane array. These new Optical Lumped Element (OLE) MKID arrays have significant advantages over semiconductor detectors like charge coupled devices (CCDs). They can count individual photons with essentially no false counts and determine the energy and arrival time of every photon with good quantum efficiency. Their physical pixel size and maximum count rate is well matched with large telescopes. These capabilities enable powerful new astrophysical instruments usable from the ground and space. MKIDs could eventually supplant semiconductor detectors for most astronomical instrumentation, and will be useful for other disciplines such as quantum optics and biological imaging.