  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)
