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LWA1 is a new radio telescope operating in the frequency range 10-88 MHz, located in central New Mexico. The telescope consists of 258 pairs of dipole-type antennas whose outputs are individually digitized and formed into beams. Simultaneously, signals from all dipoles can be recorded using one of the instrument's “all dipoles” modes, facilitating all-sky imaging. Notable features of the instrument include high intrinsic sensitivity (≈ 6 kJy zenith system equivalent flux density), large instantaneous bandwidth (up to 78 MHz), and four independently steerable beams utilizing digital “true time delay” beamforming. This paper summarizes the design of LWA1 and its performance as determined in commissioning experiments. We describe the method currently in use for array calibration, and report on measurements of sensitivity and beamwidth.