We present the discovery of the radio afterglow and near-infrared (NIR) counterpart of the Swift short gamma-ray burst (GRB) GRB 200522A, located at a small projected offset of 1 kpc from the center of a young, star-forming host galaxy at z = 0.5536. The radio and X-ray luminosities of the afterglow are consistent with those of on-axis cosmological short GRBs. The NIR counterpart, revealed by our Hubble Space Telescope observations at a rest-frame time of 2.3 days, has a luminosity of (1.3-1.7) × 1042 erg s−1. This is substantially lower than on-axis short GRB afterglow detections but is a factor of 8-17 more luminous than the kilonova of GW170817 and significantly more luminous than any kilonova candidate for which comparable observations exist. The combination of the counterpart's color (i − y = −0.08 0.21; rest frame) and luminosity cannot be explained by standard radioactive heating alone. We present two scenarios to interpret the broadband behavior of GRB 200522A: a synchrotron forward shock with a luminous kilonova (potentially boosted by magnetar energy deposition), or forward and reverse shocks from a 14°, relativistic (Γ0 10) jet. Models that include a combination of enhanced radioactive heating rates, low-lanthanide mass fractions, or additional sources of heating from late-time central engine activity may provide viable alternate explanations. If a stable magnetar was indeed produced in GRB 200522A, we predict that late-time radio emission will be detectable starting 0.3-6 yr after the burst for a deposited energy of 1053 erg. Counterparts of similar luminosity to GRB 200522A associated with gravitational wave events will be detectable with current optical searches to 250 Mpc.