We present results from a 479.7 ks Chandra exposure of the Hubble Deep Field North (HDF-N) and its immediate vicinity. In our X-ray image, the deepest ever reported with a 0.5-2.0 keV flux limit of about 4.9 x 10^{-17} erg/cm^2/s, we detect four new HDF-N X-ray sources bringing the total number of such sources to 12. The new sources include two optically bright (R=18.3-18.8), low-redshift (z<0.15) galaxies, a Fanaroff-Riley I radio galaxy, and an edge-on spiral hosting either a powerful starburst or a low-luminosity active galactic nucleus (AGN). Notably, we have now detected X-ray emission from all luminous galaxies (M_V<-18) with z<0.15 known in the HDF-N. We have also detected the remarkable microJy radio source VLA J123642.09+621331.4, which is located just outside the HDF-N and has a likely redshift of z=4.424. We have detected X-ray variability from two of the previously known HDF-N X-ray sources, and spectral fitting shows clear evidence for X-ray absorption in the brightest X-ray source in the HDF-N, a z=0.960 broad-line AGN with associated Mg II absorption. Stacking analyses of optically bright HDF-N galaxies not individually detected in X-rays have provided estimates of their average X-ray fluxes, and we find that the X-ray luminosities of `normal spirals at z~0.5 are not more than a factor of ~2 larger (per unit B-band luminosity) than those of spirals in the local Universe (z<0.01). This constrains models for the evolution of low-mass X-ray binary populations in galaxies in response to the declining cosmic star-formation rate. Monte-Carlo simulations support the validity of the stacking analyses and show that the Chandra Advanced CCD Imaging Spectrometer (ACIS) performs source detection well even with effective exposure times of ~8 Ms. (Abridged)
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