We present results from deep X-ray stacking of > 4000 high redshift galaxies from z \approx 1 to 8 using the 4 Ms Chandra Deep Field South ( CDF-S ) data , the deepest X-ray survey of the extragalactic sky to date . The galaxy samples were selected using the Lyman break technique based primarily on recent HST ACS and WFC3 observations . Based on such high specific star formation rates ( sSFRs ) : \log SFR/ M _ { * } > -8.7 , we expect that the observed properties of these LBGs are dominated by young stellar populations . The X-ray emission in LBGs , eliminating individually detected X-ray sources ( potential AGN ) , is expected to be powered by X-ray binaries and hot gas . We find , for the first time , evidence of evolution in the X-ray/SFR relation . Based on X-ray stacking analyses for z < 4 LBGs ( covering \sim 90 % of the Universe ’ s history ) , we find that the 2–10 keV X-ray luminosity evolves weakly with redshift ( z ) and SFR as : \log L _ { X } = 0.93 \log ( 1 + z ) +0.65 \log { SFR } +39.80 . By comparing our observations with sophisticated X-ray binary population synthesis models , we interpret that the redshift evolution of L _ { X } /SFR is driven by metallicity evolution in HMXBs , likely the dominant population in these high sSFR galaxies . We also compare these models with our observations of X-ray luminosity density ( total 2–10 keV luminosity per Mpc ^ { 3 } ) and find excellent agreement . While there are no significant stacked detections at z \gtrsim 5 , we use our upper limits from 5 \lesssim z \lesssim 8 LBGs to constrain the SMBH accretion history of the Universe around the epoch of reionization .