We report the X-ray detection of two z>1.4 infrared-selected galaxy clusters from the IRAC Shallow Cluster Survey (ISCS). We present new data from the Hubble Space Telescope and the W. M. Keck Observatory that spectroscopically confirm cluster ISCS J1432.4+3250 at z=1.49, the most distant of 18 confirmed z>1 clusters in the ISCS to date. We also present new spectroscopy for ISCS J1438.1+3414, previously reported at z = 1.41, and measure its dynamical mass. Clusters ISCS J1432.4+3250 and ISCS J1438.1+3414 are detected in 36ks and 143ks Chandra exposures at significances of 5.2 sigma and 9.7 sigma, from which we measure total masses of log(M_{200,Lx}/Msun) = 14.4 +/- 0.2 and 14.35^{+0.14}_{-0.11}, respectively. The consistency of the X-ray and dynamical properties of these high redshift clusters further demonstrates that the ISCS is robustly detecting massive clusters to at least z = 1.5.