  We explore the predictions of the standard hierarchical clustering scenario
of galaxy formation, regarding the numbers and metallicities of PopIII stars
likely to be found within our Galaxy today. By PopIII we shall be referring to
stars formed at large redshift ($z>4$), with low metallicities
($[Z/Z_{\odot}]<-2.5$) and in small systems (total mass $\simlt$ $2\times
10^{8} M_{\odot}$) that are extremely sensitive to stellar feedback, and which
through a prescribed merging history (Lacey & Cole 1993) end up becoming part
of the Milky Way today. An analytic, extended Press-Schechter formalism is used
to get the mass functions of halos which will host PopIII stars at a given
redshift, and which will end up in Milky Way sized systems today. Each of these
is modeled as a mini galaxy, with a detailed treatment of the dark halo
structure, angular momentum distribution, final gas temperature and disk
instabilities, all of which determine the fraction of the baryons which are
subject to star formation. Use of new primordial metallicity stellar
evolutionary models allows us to trace the history of the stars formed, give
accurate estimates of their expected numbers today, and their location in
$L/L_{\odot}$ vs. $T/K$ HR diagrams. A first comparison with observational data
suggests that the IMF of the first stars was increasingly high mass weighted
towards high redshifts, levelling off at $z\simgt 9$ at a characteristic
stellar mass scale $m_s=10-15 M_\odot$.
