We have discovered an X-ray-selected galaxy cluster with a spectroscopic redshift of 1.753. The redshift is of the brightest cluster galaxy (BCG), which is coincident with the peak of the X-ray surface brightness. We also have concordant photometric redshifts for seven additional candidate cluster members. The X-ray luminosity of the cluster is (3.68 ± 0.70) × 1043 erg s-1 in the 0.1-2.4 keV band. The optical/IR properties of the BCG imply that its formation redshift was ~5 if its stars formed in a short burst. This result continues the trend from lower redshift in which the observed properties of BCGs are most simply explained by a single monolithic collapse at very high redshift instead of the theoretically preferred gradual hierarchical assembly at later times. However, the models corresponding to different formation redshifts are more clearly separated as our observation epoch approaches the galaxy formation epoch. Although our infrared photometry is not deep enough to define a red sequence, we do identify a few galaxies at the cluster redshift that have the expected red sequence photometric properties.