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We confirm spectroscopically the existence of a population of galaxies atz>~2 with rest-frame optical colors similar to normal nearby galaxies. Thegalaxies were identified by their red near-infrared colors in deep imagesobtained with ISAAC on the Very Large Telescope. Redshifts of six galaxies withJs-Ks>2.3 were measured from optical spectra obtained with the Keck Telescope.Five out of six are in the range 2.43<=z<=3.52, demonstrating that the Js-Kscolor selection is quite efficient. The rest-frame ultraviolet spectra ofconfirmed z>2 galaxies display a range of properties, with two galaxies showingemission lines characteristic of AGN, two having Ly-alpha in emission, and oneshowing interstellar absorption lines only. Their full spectral energydistributions are well described by constant star formation models with ages1.4-2.6 Gyr, except for one galaxy whose colors indicate a dusty starburst. Theconfirmed z>2 galaxies are very luminous, with Ks=19.2-19.9. Assuming that ourbright spectroscopic sample is representative for the general population ofJs-Ks selected objects, we find that the surface density of red z>~2 galaxiesis ~0.9/arcmin^2 to Ks=21. The surface density is comparable to that ofLyman-break selected galaxies with Ks<21, when corrections are made for thedifferent redshift distributions of the two samples. Although there will besome overlap between the two populations, most 'optical-break' galaxies are toofaint in the rest-frame ultraviolet to be selected as Lyman-break galaxies. Themost straightforward interpretation is that star formation in typicaloptical-break galaxies started earlier than in typical Lyman-break galaxies.Optical-break galaxies may be the oldest and most massive galaxies yetidentified at z>2, and could evolve into early-type galaxies and bulges.Comment: Accepted for publication in the Astrophysical Journal Letters. (see  also papers by Franx et al. and Daddi et al. in this listing

Spectroscopic Confirmation of a Substantial Population of Luminous Red Galaxies at Redshifts z 2