We present Chandra X-ray observations of the radio-quiet QSO PG 2302+029. This quasar has a rare system of ultra-high-velocity (À56,000 km s À1 ) UV absorption lines that form in an outflow from the active nucleus. The Chandra data indicate that soft X-ray absorption is also present. We perform a joint UV and X-ray analysis, using photoionization calculations, to determine the nature of the absorbing gas. The UV and X-ray data sets were not obtained simultaneously. Nonetheless, our analysis suggests that the X-ray absorption occurs at high velocities in the same general region as the UV absorber. There are not enough constraints to rule out multizone models. In fact, the distinct broad and narrow UV line profiles clearly indicate that multiple zones are present. Our preferred estimates of the ionization and total column density in the X-ray absorber (log U ¼ 1:6, N H ¼ 10 22:4 cm À2 ) overpredict the O vi 1032, 1038 absorption unless the X-ray absorber is also outflowing at $56,000 km s À1 , but they overpredict the Ne viii 770, 780 absorption at all velocities. If we assume that the X-ray-absorbing gas is outflowing at the same velocity as the UVabsorbing wind and that the wind is radiatively accelerated, then the outflow must be launched at a radius of 10 15 cm from the central continuum source. The smallness of this radius casts doubts on the assumption of radiative acceleration.