We employ X-ray stacking techniques to examine the contribution from X-ray undetected , mid-infrared–selected sources to the unresolved , hard ( 6 - 8 keV ) cosmic X-ray background ( CXB ) . We use the publicly available , 24 \mu m Spitzer Space Telescope MIPS catalogs from the Great Observatories Origins Deep Survey ( GOODS ) - North and South fields , which are centered on the 2 Ms Chandra Deep Field-North and the 1 Ms Chandra Deep Field-South , to identify bright ( S _ { 24 \mu { m } } > 80 \mu Jy ) mid-infrared sources that may be powered by heavily obscured AGNs . We measure a significant stacked X-ray signal in all of the X-ray bands examined , including , for the first time , a significant ( 3.2 \sigma ) 6 - 8 keV stacked X-ray signal from an X-ray undetected source population . We find that the X-ray-undetected MIPS sources make up about 2 \% ( or less ) of the total CXB below 6 keV , but about 6 \% in the 6 - 8 keV band . The 0.5 - 8 keV stacked X-ray spectrum is consistent with a hard power-law ( \Gamma = 1.44 \pm 0.07 ) , with the spectrum hardening at higher X-ray energies . Our findings show that these bright MIPS sources do contain obscured AGNs , but are not the primary source of the unresolved 50 \% of 6 - 8 keV CXB . Our study rules out obscured , luminous QSOs as a significant source of the remaining unresolved CXB and suggests that it most likely arises from a large population of obscured , high-redshift ( z \lower 2.0 pt \hbox { $ \buildrel \scriptstyle > \over { \scriptstyle \sim } $ } 1 ) , Seyfert-luminosity AGNs .