We present results from a 221.9 ks Chandra exposure of the HDF-N and its vicinity, concentrating on the 8.6 X 8.7 area covered by the Caltech Faint Field Galaxy Redshift Survey (the `Caltech area). The minimum detectable fluxes in the 0.5-2 keV and 2-8 keV bands are 1.3e-16 cgs and 6.5e-16 cgs, respectively and a total of 82 sources are detected. More than 80% of the extragalactic X-ray background in the 2-8 keV band is resolved. Redshifts are available for 96% of the sources with R<23; the redshift range is 0.1-3.5 with most sources having z < 1.5. Eight of the X-ray sources are located in the HDF-N itself, including two not previously reported. A population of X-ray faint, optically bright, nearby galaxies emerges at soft-band fluxes of ~< 3e-16 cgs. We set the tightest constraints to date on the X-ray emission properties of microJy radio sources, mid-infrared sources detected by ISO, and very red (R-K_s > 5.0) objects. Where both the infrared and the X-ray coverage are deepest, 75% of the X-ray sources are detected by ISO; the high X-ray to infrared matching rate bodes well for future sensitive infrared observations of faint X-ray sources. Four of the 33 very red objects that have been identified in the Caltech area by Hogg et al. (2000) are detected in X-rays; these four are among our hardest Chandra sources, and we argue that they contain moderately luminous obscured AGN. Overall, however, the small Chandra detection fraction suggests a relatively small AGN content in the optically selected very red object population. (Abridged)
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