We present a focused X-ray and multiwavelength study of the ultraluminous weak-line quasar (WLQ) SDSS J1521+5202, one of the few X-ray weak WLQs that is amenable to basic X-ray spectral and variability investigations. J1521+5202 shows striking X-ray variability during 2006–2023, by up to a factor of ≈32 in 0.5–2 keV flux, and our new 2023 Chandra observation caught it in its brightest X-ray flux state to date. Concurrent infrared/optical observations show only mild variability. The 2023 Chandra spectrum can be acceptably described by a power law with intrinsic X-ray absorption, and it reveals a nominal intrinsic level of X-ray emission relative to its optical/ultraviolet emission. In contrast, an earlier Chandra spectrum from 2013 shows apparent spectral complexity that is not well fit by a variety of models, including ionized absorption or standard Compton-reflection models. Overall, the observations are consistent with the thick-disk plus outflow model previously advanced for WLQs, where a nominal level of underlying X-ray emission plus variable absorption leads to the remarkable observed X-ray variability. In the case of J1521+5202, it appears likely that the outflow, and not the thick disk itself, lies along our line of sight and causes the X-ray absorption.