  Context. We have recently investigated the origin of chemical signatures
observed in Galactic halo stars by means of a stochastic chemical evolution
model. We have found that rotating massive stars are a promising way to explain
several signatures observed in these fossil stars. Aims. In the present paper
we discuss how the extremely metal-poor halo star TYC 8442-1036-1, for which we
have now obtained detailed abundances from VLT-UVES spectra, fits into the
framework of our previous work. Methods. We apply a standard 1D LTE analysis to
the spectrum of this star. We measure the abundances of 14 chemical elements;
for Na, Mg, Ca, Sc, Ti, V, Cr, Mn, Fe, Ni and Zn we compute the abundances
using equivalent widths; for C, Sr and Ba we obtain the abundances by means of
synthetic spectra generated by MOOG. Results. We find an abundance of [Fe/H]=
$-$3.5 $\pm$0.13 dex based on our high resolution spectrum; this points to an
iron content lower by a factor of three (0.5 dex) compared to the one obtained
by a low resolution spectrum. The star has a [C/Fe] = 0.4 dex, and it is not
carbon enhanced like most of the stars at this metallicity. Moreover, this star
lies in the plane [Ba/Fe] vs. [Fe/H] in a relatively unusual position, shared
by a few others galactic halo stars that is only marginally explained by our
past results. Conclusions. The comparison of the model results with the
chemical abundance characteristics of this group of stars can be improved if we
consider in our model the presence of faint supernovae coupled with rotating
massive stars. These results seem to imply that rotating massive stars and
faint supernovae scenarios are complementary to each other, and are both
required in order to match the observed chemistry of the earliest phases of the
chemical enrichment of the Universe.
