  The number density and clustering properties of Lyman-break galaxies (LBGs)
observed at redshift $z\sim 3$ are best explained by assuming that they are
associated with the most massive haloes at $z\sim 3$ predicted in hierarchical
models of structure formation. In this paper we study, under the same
assumption, how star formation and chemical enrichment may have proceeded in
the LBG population. A consistent model, in which the amount of cold gas
available for star formation must be regulated, is suggested. It is found that
gas cooling in dark haloes provides a natural regulation process. In this
model, the star formation rate in an LBG host halo is roughly constant over
about 1 Gyr. The predicted star formation rates and effective radii are
consistent with observations. The metallicity of the gas associated with an LBG
is roughly equal to the chemical yield, or about the order of $1 Z_{\odot}$ for
a Salpeter IMF. The contribution to the total metals of LBGs is roughly
consistent with that obtained from the observed cosmic star formation history.
The model predicts a marked radial metallicity gradient in a galaxy, with the
gas in the outer region having much lower metallicity. As a result, the
metallicities for the damped Lyman-alpha absorption systems expected from the
LBG population are low. Since LBG halos are filled with hot gas in this model,
their contributions to the soft X-ray background and to the UV ionization
background are calculated and discussed.
