We report the discovery of X-ray broad absorption lines ( BALs ) from the BALQSO APM 08279+5255 originating from material moving at relativistic velocities with respect to the central source . The large flux magnification by a factor of \sim 100 provided by the gravitational lens effect combined with the large redshift ( z = 3.91 ) of the quasar have facilitated the acquisition of the first high signal-to-noise X-ray spectrum of a quasar containing X-ray BALs . Our analysis of the X-ray spectrum of APM 08279+5255 places the rest-frame energies of the two observed absorption lines at 8.1 and 9.8 keV . The detection of each of these lines is significant at the > 99.9 % confidence level based on the F -test . Assuming that the absorption lines are from Fe xxv K { \alpha } , the implied bulk velocities of the X-ray BALs are \sim 0.2 c and \sim 0.4 c , respectively . The observed high bulk velocities of the X-ray BALs combined with the relatively short recombination time-scales of the X-ray absorbing gas imply that the absorbers responsible for the X-ray BALs are located at radii of \buildrel \scriptstyle < \over { \scriptstyle \sim } 2 \times 10 ^ { 17 } cm , within the expected location of the UV absorber . With this implied geometry the X-ray gas could provide the necessary shielding to prevent the UV absorber from being completely ionized by the central X-ray source , consistent with hydrodynamical simulations of line-driven disk winds . Estimated mass-outflow rates for the gas creating the X-ray BALs are typically less than a solar mass per year . Our spectral analysis also indicates that the continuum X-ray emission of APM 08279+5255 is consistent with that of a typical radio-quiet quasar with a spectral slope of \Gamma = 1.72 _ { -0.05 } ^ { +0.06 } .