  We describe the X-ray properties of a large sample of $z\sim3$ 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 $L_{\rm UV}/L_{\rm X}$, 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 (truncated).
