  Recent studies have shown that distant red galaxies (DRGs), which dominate
the high-mass end of the galaxy population at z~2.5, are more strongly
clustered than the population of blue star-forming galaxies at similar
redshifts. However these studies have been severely hampered by the small sizes
of fields having deep near-infrared imaging. Here we use the large UKIDSS Ultra
Deep Survey to study the clustering of DRGs. The size and depth of this survey
allows for an unprecedented measurement of the angular clustering of DRGs at
2<z_phot<3 and K<21. The correlation function shows the expected power law
behavior, but with an apparent upturn at theta<~10". We deproject the angular
clustering to infer the spatial correlation length, finding 10.6+-1.6 h^-1 Mpc.
We use the halo occupation distribution framework to demonstrate that the
observed strong clustering of DRGs is not consistent with standard models of
galaxy clustering, confirming previous suggestions that were based on smaller
samples. Inaccurate photometric redshifts could artificially enhance the
observed clustering, however significant systematic redshift errors would be
required to bring the measurements into agreement with the models. Another
possibility is that the underlying assumption that galaxies interact with their
large-scale environment only through halo mass is not valid, and that other
factors drive the evolution of the oldest, most massive galaxies at z~2.
