We report the results of our efforts to track down the source population responsible for the unresolved 6-8 keV cosmic X-ray background (XRB). Using the 4 Ms Chandra Deep Field-South (CDF-S) survey, we have identified a sample of ~6800 X-ray undetected galaxies that dominates the unresolved 20-25% of the 6-8 keV XRB. This sample was constructed by applying mass and color cuts to sources from a parent catalog based on GOODS-South HST z-band imaging of the central 6-arcmin-radius area of the 4 Ms CDF-S. The stacked 6-8 keV detection is significant at the 3.9 sigma level, but the stacked emission was not detected in the 4-6 keV band which indicates the existence of an underlying population of highly obscured active galactic nuclei (AGNs). Further examinations of these 6800 galaxies indicate that the galaxies with redshifts of 1<z<2, magnitudes of 25<z850<27, and masses of 2E8<Mstar/Msun<2E9 make the majority contributions to the unresolved 6-8 keV XRB. Such a population is seemingly surprising given that the majority of the X-ray detected AGNs reside in massive (> 10^10 Msun) galaxies. We discuss constraints upon this underlying AGN population, supporting evidence for relatively low-mass galaxies hosting highly obscured AGNs, and prospects of further boosting the stacked signal.