  We investigate the conditions under which the first low-mass stars formed in
the universe by confronting theoretical predictions governing the transition
from massive Population III to low-mass Population II stars with recent
observational C and/or O abundance data of metal-poor Galactic stars. Based on
an existing theory, we introduce a new "observer-friendly" function, the
transition discriminant D_trans, which provides empirical constraints as well
as a powerful comparison between the currently available data of metal-poor
halo stars and theoretical predictions of the formation of the first low-mass
stars (<1 M_sun). Specifically, we compare the empirical stellar results with
the theory that fine-structure lines of C and O dominate the transition from
Pop III to Pop II in the early universe. We find the observational data for
halo objects as well as for dSph galaxies and globular clusters to be
consistent with this theory. An explanation for the observed lack of metal-poor
stars in dSph galaxies and globular clusters is also suggested. Finally, we
predict that any star to be found with [Fe/H]<-4 should have enhanced C and/or
O abundances. The high C and O abundances of the two most iron-poor stars are
in line with our prediction.
