We present results from stacking analyses, using the I Ms Chandra Deep Fiel
d-North data, that constrain the X-ray emission of Lyman break galaxies at
z approximate to 2-4. Stacking the counts from 24 individually undetected L
yman break galaxies located within the Hubble Deep Field-North, we have obt
ained average detections of these objects in the resulting 0.5-8.0 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 si
gnificant. The average rest-frame 2-8 keV luminosity of a Lyman break galax
y is derived to be approximate to3.2 x 10(41) ergs s(-1), comparable to tha
t 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 t
han that seen from local starbursts. The X-ray emission probably arises fro
m a combination of high-mass X-ray binaries, "super-Eddington" X-ray source
s, and low-luminosity active galactic nuclei.