The publicly available EIS-DEEP optical-NIR data for the AXAF (Chandra) Deep Field have been used to construct samples of Extremely Red Objects (EROs) using various single-band and multi-band color criteria. In this work we define as EROs objects with colors consistent with passively evolving elliptical galaxies at z $geq$ 1. The EROs surface densities we derive are intermediate between previous published values, emphasizing again the need for larger survey areas to constrain the effects of possible large-scale structure. Although various single-color selected samples can be derived, the EROs sample selected using R-Ks > 5, I-Ks > 4, J-Ks > 1.8 jointly is likely to contain the highest fraction of passively evolving luminous field elliptical galaxies at z >= 1, or conversely, the lowest fraction of lower redshift interlopers. The surface density of this multi-band selected EROs sample is consistent with the conclusion that little or no field elliptical volume density evolution has occurred in the redshift range 0 > z > 1.5. However, extensive spectroscopic followup is necessary to confirm this conclusion.
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