We describe the X-ray properties of a large sample of z \sim 3 Lyman Break Galaxies ( LBGs ) in the region of the Hubble Deep Field North , derived from the 1 Ms public Chandra observation . Of our sample of 148 LBGs , four are detected individually . This immediately gives a measure of the bright AGN fraction in these galaxies of \sim 3 per cent , which is in agreement with that derived from the UV spectra . The X-ray color of the detected sources indicates that they are probably moderately obscured . Stacking of the remainder shows a significant detection ( 6 \sigma ) with an average luminosity of 3.5 \times 10 ^ { 41 } erg s ^ { -1 } per galaxy in the rest frame 2-10 keV band . We have also studied a comparison sample of 95 z \sim 1 “ Balmer Break ” galaxies . Eight of these are detected directly , with at least two clear AGN based on their high X-ray luminosity and very hard X-ray spectra respectively . The remainder are of relatively low luminosity ( < 10 ^ { 42 } erg s ^ { -1 } ) , and the X-rays could arise from either AGN or rapid star-formation . The X-ray colors and evidence from other wavebands favor the latter interpretation . Excluding the clear AGN , we deduce a mean X-ray luminosity of 6.6 \times 10 ^ { 40 } erg s ^ { -1 } , a factor \sim 5 lower than the LBGs . The average ratio of the UV and X-ray luminosities of these starforming galaxies L _ { UV } / L _ { X } , however , is approximately the same at z = 1 as it is at z = 3 . This scaling implies that the X-ray emission follows the current star formation rate , as measured by the UV luminosity . We use our results to constrain the star formation rate at z \sim 3 from an X-ray perspective . Assuming the locally established correlation between X-ray and far-IR luminosity , the average inferred star formation rate in each Lyman break galaxy is found to be approximately 60 M _ { \odot } /yr , in excellent agreement with the extinction-corrected UV estimates . This provides an external check on the UV estimates of the star formation rates , and on the use of X-ray luminosities to infer these rates in rapidly starforming galaxies at high redshift .