The Cosmic InfraRed Background (CIRB) is the sum total of the redshifted and reprocessed short wavelength radiation from the era of galaxy formation, and hence contains vital information about the history of galactic evolution. One of the main problems associated with estimating an isotropic CIRB in the near infrared (1-5 microns) is the unknown contribution from stars within our own galaxy. The optimal observational window to search for a background in the near-IR is at 3.5 microns since that is the wavelength region where the other main foreground, the zodiacal dust emission, is the least. It is not possible to map out the entire 3.5 micron sky at a resolution which will accurately estimate the flux from stars. However, since the CIRB is presumably isotropic, it can potentially be detected by selecting a smaller field and imaging it at good resolution to estimate the stellar intensity. We selected a 2x2 degree dark spot near the North Galactic Pole which had the least intensity at 3.5 microns after a zodiacal light model was subtracted from the all-sky maps generated by the Diffuse InfraRed Background Experiment (DIRBE). The measured total intensity of the few bright stars in this field was combined with a model for the contribution from dimmer stars and subtracted from the zodi-subtracted DIRBE map. The contribution from the interstellar medium was also subtracted leaving a residual intensity at 2.2 microns of: 16.4+/-4.4 kJy/sr or 22.4+/-6 nW/m^2/sr, and at 3.5 microns: 12.8+/-3.8 kJy/sr or 11+/-3.3 nW/m^2/sr. [Abridged]
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