We present a high resolution ( \lambda / \Delta \lambda \approx 500 ) X-ray spectrum of the bright quasar H1821+643 ( z = 0.297 ) , obtained in a 470 ksec observation with the Chandra X-ray Observatory . We search for X-ray absorption by highly ionized metal species , O vii and O viii in particular , at the redshifts of the six intervening O vi absorption systems known from UV studies . We detect features with \gtrsim 2 \sigma significance at the predicted O vii and O viii wavelengths of one O vi system , at the O vii wavelength of a second , and at the Ne ix wavelength of a third . We find two additional features of comparable strength ( one O vii and one O viii ) within 1000 km s ^ { -1 } of O vi redshifts . The 1 \sigma constraints on the relative abundances of different species imply significant variations from system to system in f ( { { O } \hbox { { \sc vi } } } ) , the fraction of oxygen in the O vi state . The constraints in the two detected O vi systems imply gas overdensities lower than the values \delta \gtrsim 100 expected in virialized systems , suggesting that the absorption arises in lower density , filamentary structures . At the 2 \sigma level , however , the physical constraints are weak , though all of the systems must have temperature T < 10 ^ { 6 } { K } to be consistent with upper limits on O vii . If we treat our 2 \sigma detections of known O vi systems as real , but assume minimal O vii and O viii in the other systems , we estimate [ f ( { { O } \hbox { { \sc vi } } } ) + f ( { { O } \hbox { { \sc vii } } } ) + f ( { { O } % \hbox { { \sc viii } } } ) ] / f ( { { O } \hbox { { \sc vi } } } ) = 32 \pm 9 for the average ratio of all highly ionized oxygen species to O vi . Combined with estimates of the total column density of O vi absorption per unit redshift , this ratio implies that the total baryon fraction associated with detected O vi absorbers is \Omega _ { b } ( { { O } \hbox { { \sc vi } } } ) \sim 0.03 h _ { 70 } ^ { -1 } , a substantial fraction of the baryon density predicted by big bang nucleosynthesis , and larger than that associated with stars or with gas detected in 21cm or X-ray emission . Because of the limited S/N of the detections , these results must be treated with caution . Nonetheless , the combination of the O vi data with these X-ray forest measurements provides the most direct evidence to date for the pervasive , moderate density , shock-heated intergalactic medium predicted by leading cosmological scenarios . The high inferred incidence of relatively strong O vii and O viii absorption implies that some regions of this medium are enriched to a level substantially above [ { O / H } ] = -1 .