We present Chandra X-ray observations of the radio-quiet QSO PG 2302029. This quasar has a rare system of ultra-high velocity (-56,000 km s(exp -1) 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 datasets 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 multi-zone 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 (logU = 1.6, N(sub eta) = 10(exp 22.4) cm (exp -2) over predict the O VI lambda lambda1032,1038 absorption unless the X-ray absorber is also outflowing at approximately 56,000 km s(exp-l), but they over predict the Ne VIII lambda lambda 770,780 absorption at all velocities. If we assume that the X-ray absorbing gas is outflowing at the same velocity of the UV-absorbing wind and that the wind is radiatively accelerated, then the outflow must be launched at a radius of less than or equal to 10(exp 15) cm from the central continuum source. The smallness of this radius casts doubts on the assumption of radiative acceleration.