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We analyzed the spatial distribution of 28500 photometrically selected galaxies with AB magnitude 23.5<R<25.5 and redshift 1.4<z<3.5 in 21 fields with a total area of 0.81 square degrees. The galaxies were divided into three subsamples, with mean redshifts z=1.7, 2.2, 2.9, according to the UGR selection criteria of Adelberger et al. (2004) and Steidel et al. (2003). Combining the galaxies' measured angular clustering with redshift distributions inferred from 1600 spectroscopic redshifts, we find comoving correlation lengths at the three redshifts of r_0 = 4.5+-0.6, 4.2+-0.5, and 4.0+-0.6 h^-1 Mpc, respectively, and infer a roughly constant correlation function slope of gamma=1.6+-0.1. We derive similar numbers from the 1600 object spectroscopic sample itself with a new statistic, K, that is insensitive to many possible systematics. Galaxies that are bright in R (lambda_rest ~ 1500-2500A) cluster more strongly than fainter galaxies at z=2.9 and z=2.2 but not, apparently, at z=1.7. Comparison to a numerical simulation that is consistent with recent WMAP observations suggests that galaxies in our samples are associated with dark matter halos of mass ~ 10^12, and that a small fraction of the halos contain more than one galaxy that satisfies our selection criteria. Adding recent observations of galaxy clustering at z~0 and z~1 to the simulation results, we conclude that the typical object in our samples will evolve into an elliptical galaxy by redshift z=0 and will already have an early-type spectrum by redshift z=1. We comment briefly on the implied relationship between galaxies in our survey and those selected with other techniques. (slightly abridged)