The %1 Ms Chandra Deep Field North observation is used to study the extended X-ray sources in the region surrounding the Hubble Deep Field North (HDF-N), yielding the most sensitive probe of extended X-ray emission at cosmological distances to date. A total of six such sources are detected, the majority of which align with small numbers of optically bright galaxies. Their angular sizes, band ratios, and X-ray luminosities-assuming they lie at the same distances as the galaxies coincident with the X-ray emission-are generally consistent with the properties found for nearby groups of galaxies. One source is notably different and is likely to be a poor-to-moderate X-ray cluster at high redshift (i.e., z & 0.7). This source has a large angular extent, a double-peaked X-ray morphology, and an overdensity of unusual objects [very red objects, optically faint (I ! 24) radio and X-ray sources]. Another of the six sources is coincident with several z % 1.01 galaxies located within the HDF-N itself, including the FR I radio galaxy VLA J123644+621133, and is likely to be a group or poor cluster of galaxies at that redshift. We are also able to place strong constraints on the optically detected cluster of galaxies ClG 1236+6215 at z = 0.85 and the wide-angle-tailed radio galaxy VLA J123725+621128 at z $ 1-2; both sources are expected to have considerable associated diffuse X-ray emission, and yet they have rest-frame 0.5-2.0 keV X-ray luminosities of .3 Â 10 42 and .(3-15) Â 10 42 ergs s À1 , respectively. The environments of both sources are either likely to have a significant deficit of hot intracluster gas compared with local clusters of galaxies, or they are X-ray groups. We find the surface density of extended X-ray sources in this observation to be 167 þ97 À67 deg À2 at a limiting soft-band flux of %3 Â 10 À16 ergs cm À2 s À1 . No evolution in the X-ray luminosity function of clusters is needed to explain this value.