New information on the relations between the Galactic disks, the halo, and satellite galaxies is being obtained from elemental abundances of stars having metallicities in the range −1.5 < [Fe/H] < −0.5. The first results for a sample of 26 halo stars and 13 thick-disk stars observed with the ESO VLT/UVES spectrograph are presented. The halo stars fall in two distinct groups: one group (9 stars) has [α/Fe] = 0.30 ± 0.03 like the thick-disk stars. The other group (17 stars) shows a clearly deviating trend ranging from [α/Fe] = 0.20 at [Fe/H] = −1.3 to [α/Fe] = 0.08 at [Fe/H] = −0.8. The kinematics of the stars are discussed and the abundance ratios Na/Fe, Ni/Fe, Cu/Fe and Ba/Y are applied to see if the “low-alpha” stars are connected to the thin disk or to Milky Way satellite galaxies. Furthermore, we compare our data with simulations of chemical abundance distributions in hierarchically formed stellar halos in a ΛCDM Universe.