The early history of metal enrichment in the galactic halo was studied. We
investigated the chemical inhomogeneity by using a stochastic chemical evol
ution model. The model confronts the metallicity distribution function of l
ong-lived halo stars, which has been found to be a clue to obtain the best
model prescriptions. We have found that star formation in the halo virtuall
y terminated by similar to 1 Gyr and that the halo has never been chemicall
y homogeneous in its star-formation history. This conclusion does not depen
d whether the mass loss from the halo is taken into account or not. The obs
erved ratios of alpha-elements with respect to iron do not show scatters on
a [alpha/Fe]-[Fe/H] plane, but this does not imply that interstellar matte
r in the halo was homogeneous because a chemical evolution path on this dia
gram is degenerate in the star-formation rate. On the other hand, an appare
nt spread of the [Sr/Fe] ratio among metal-poor halo stars does not reflect
an inhomogeneous metal enrichment; instead, it is due to a sharp increase
in the production rate of strontium, which is probably synthesised in sligh
tly less-massive stars than the progenitor of iron-producing type II supern
ovae.