  An early history of metal enrichment in the Galactic halo is studied. We
investigate chemical inhomogeneity by using a stochastic chemical evolution
model. The model confronts with metallicity distribution function of long-lived
halo stars which is found to be a clue to obtain the best model prescriptions.
We find that the star formation in the halo virtually terminated by around 1
Gyr and that the halo has never been chemically homogeneous in its star
formation history. This conclusion does not depend whether mass loss from the
halo is taken into account or not. Observed 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 matter in the halo was homogeneous because a
chemical evolution path on this diagram is degenerate in the star formation
rate. On the other hand, apparent spread of [Sr/Fe] ratio among metal-poor halo
stars does not reflect an inhomogeneous metal enrichment, instead it is due to
a sharp increase in a production rate of strontium that is probably synthesised
in slightly less massive stars than progenitor of iron-producing SNII.
