We investigate the intrinsic scatter in the chemical abundances of a sample of metal-poor ([Fe/H]<-2.5) Milky Way halo stars. We draw our sample from four historic surveys and focus our attention on the stellar Mg, Ca, Ni, and Fe abundances. Using these elements, we investigate the chemical enrichment of these metal-poor stars using a model of stochastic chemical enrichment. Assuming that these stars have been enriched by the first generation of massive metal-free stars, we consider the mass distribution of the enriching population alongside the stellar mixing and explosion energy of their supernovae. For our choice of stellar yields, our model suggests that the most metal-poor stars were enriched, on average, by N*=5^{+13}_{-3} (1 sigma) Population III stars. This is comparable to the number of enriching stars inferred for the most metal-poor DLAs. Our analysis therefore suggests that some of the lowest mass structures at z~3 contain the chemical products from <13 (2 sigma) Population III enriched minihaloes. The inferred IMF is consistent with that of a Salpeter distribution and there is a preference towards ejecta from minimally mixed hypernovae. However, the estimated enrichment model is sensitive to small changes in the stellar sample. An offset of ~0.1 dex in the [Mg/Ca] abundance is shown to be sensitive to the inferred number of enriching stars. We suggest that this method has the potential to constrain the multiplicity of the first generation of stars, but this will require: (1) a stellar sample whose systematic errors are well understood; and, (2) documented uncertainties associated with nucleosynthetic yields.
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