Using the 4Ms Chandra Deep Field-South (CDF-S) survey, we have identified a sample of 6845 X-ray-undetected galaxies that dominates the unresolved {approx}20%-25% of the 6-8keV cosmic X-ray background (XRB). This sample was constructed by applying mass and color cuts to sources from a parent catalog based on GOODS-South Hubble Space Telescope z-band imaging of the central 6' radius area of the 4Ms CDF-S. The stacked 6-8keV detection is significant at the 3.9{sigma} level, but the stacked emission was not detected in the 4-6keV band, which indicates the existence of an underlying population of highly obscured active galactic nuclei (AGNs). Further examinations of these 6845 galaxies indicate that the galaxies on the top of the blue cloud and with redshifts of 1<~z<~3, magnitudes of 25<~z_850_<~28, and stellar masses of 2x10^8^<~M_{sstarf}_/M_{sun}_<~2x10^9^ make the majority contributions to the unresolved 6-8keV XRB. Such a population is seemingly surprising given that the majority of the X-ray-detected AGNs reside in massive (>~10^10^M_{sun}_) galaxies. We discuss constraints upon this underlying AGN population, supporting evidence for relatively low mass galaxies hosting highly obscured AGNs, and prospects for further boosting the stacked signal.