We report the detection of a massive high-redshift cluster of galaxies near the quadruple quasar RX J0911+05, using the LRIS instrument on the Keck-II telescope. The cluster is found to have a mean redshift of <z>=0.7689+/-0.002 and a velocity dispersion of sigma=836{+180-200} km/s, based on redshift measurements for 24 member galaxies. This massive high-redshift cluster is the origin of the unusually large external shear required by lensing models of the quadruple quasar system. We predict the expected time delay depending on the exact contribution of the cluster. A measurement of the time delay and further deep lensing and X-ray observations will unravel useful properties of this serendipitously discovered high-redshift cluster, and may put interesting cosmological constraints on H0.

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