We present results from stacking analyses , using the 1 Ms Chandra Deep Field North data , that constrain the X-ray emission of Lyman break galaxies at z \approx 2–4 . Stacking the counts from 24 individually undetected Lyman break galaxies located within the Hubble Deep Field North , we have obtained average detections of these objects in the resulting 0.5–8.0 keV and 0.5–2.0 keV images ; these images have effective exposure times of 22.4 Ms ( 260 days ) . Monte Carlo testing empirically shows the detections to be highly significant . The average rest-frame 2–8 keV luminosity of a Lyman break galaxy is derived to be \approx 3.2 \times 10 ^ { 41 } erg s ^ { -1 } , comparable to that of the most X-ray luminous starbursts in the local Universe . The observed ratio of X-ray to B -band luminosity is somewhat , but not greatly , higher than that seen from local starbursts . The X-ray emission probably arises from a combination of high-mass X-ray binaries , “ super-Eddington ” X-ray sources , and low-luminosity active galactic nuclei .