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 = 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 3.2 x 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.
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