We present a Hubble Space Telescope Advanced Camera for Surveys ( ACS ) weak-lensing study of RX J0849+4452 and RX J0848+4453 , the two most distant ( at z = 1.26 and z = 1.27 , respectively ) clusters yet measured with weak-lensing . The two clusters are separated by \sim 4 \arcmin from each other and appear to form a supercluster in the Lynx field . Using our deep ACS i _ { 775 } and z _ { 850 } imaging , we detected weak-lensing signals around both clusters at \sim 4 \sigma levels . The mass distribution indicated by the reconstruction map is in good spatial agreement with the cluster galaxies . From the singular isothermal sphere ( SIS ) fitting , we determined that RX J0849+4452 and RX J0848+4453 have similar projected masses of ( 2.0 \pm 0.6 ) \times 10 ^ { 14 } M _ { \sun } and ( 2.1 \pm 0.7 ) \times 10 ^ { 14 } M _ { \sun } , respectively , within a 0.5 Mpc ( \sim 60 \arcsec ) aperture radius . In order to compare the weak-lensing measurements with the X-ray results calibrated by the most recent low-energy quantum efficiency determination and time-dependent gain correction , we also re-analyzed the archival Chandra data and obtained T = 3.8 _ { -0.7 } ^ { +1.3 } and 1.7 _ { -0.4 } ^ { +0.7 } keV for RX J0849+4452 and RX J0848+4453 , respectively . Combined with the X-ray surface brightness profile measurement under the assumption of isothermal \beta model , the temperature of RX J0849+4452 predicts that the projected mass of the cluster within r = 0.5 ~ { } Mpc is 2.3 _ { -0.4 } ^ { +0.8 } \times 10 ^ { 14 } M _ { \sun } , consistent with the weak-lensing analysis . On the other hand , for RX J0848+4453 we find that the mass derived from this X-ray analysis is much smaller ( 6.3 _ { -1.5 } ^ { +2.6 } \times 10 ^ { 13 } M _ { \sun } ) than the weak-lensing measurement . One possibility for this observed discrepancy is that the intracluster medium ( ICM ) of RX J0848+4453 has not yet fully thermalized . Although this interpretation is rather simplistic , the relatively loose distribution of the cluster galaxies in part supports this possibility of low degree of virialization . We also discuss other scenarios that might give rise to the discrepancy .