The Chandra X-Ray Observatory was used to obtain a 190 ks image of three high-redshift galaxy clusters in one observation. The results of our analysis of these data are reported for the two z > 1 clusters in this Lynx field, which are the most distant known X-ray luminous clusters. Spatially extended X-ray emission was detected from both these clusters, indicating the presence of hot gas in their intracluster media. A fit to the X-ray spectrum of RX J0849 + 4452 at z = 1.26 yields a temperature of kT = 5.8(-1.7)(+2.8) keV. Using this temperature and the assumption of an isothermal sphere, the total mass of RX J0849+4452 is found to be 4.01(-1.9)(+2.4) x 10(14) h(65)(-1) M. within r = 1 h(65)(-1) Mpc. The T-X for RX J0849+4452 approximately agrees with the expectation based on its L-bol = 3.3(-0.5)(+0.9) x 10(44) ergs s(-1) according to the low-redshift L-X-T-X relation. The very different distributions of X-ray-emitting gas and of the red member galaxies in the two z > 1 clusters, in contrast to the similarity of the optical/IR colors of those galaxies, suggests that the early-type galaxies mostly formed before their host clusters.