We present Chandra X-ray observations of the radio-quiet QSO PG 2302+029 . This quasar has a rare system of ultra-high velocity ( -56 , 000 km s ^ { -1 } ) UV absorption lines that form in an outflow from the active nucleus ( Jannuzi et al . 2003 ) . 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 detemine 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 ( \log U = 1.6 , N _ { H } = 10 ^ { 22.4 } cm ^ { -2 } ) over predict the O vi \lambda \lambda 1032 , 1038 absorption unless the X-ray absorber is also outflowing at \sim 56 , 000 km s ^ { -1 } , 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 \leq 10 ^ { 15 } cm from the central continuum source . The smallness of this radius casts doubts on the assumption of radiative acceleration .