We discuss the carbon-normal and carbon-rich populations of Galactic halo stars having [ Fe/H ] \lesssim –3.0 , utilizing chemical abundances from high-resolution , high- S / N model-atmosphere analyses . The C-rich population represents \sim 28 % of stars below [ Fe/H ] = –3.1 , with the present C-rich sample comprising 16 CEMP-no stars , and two others with [ Fe/H ] \sim –5.5 and uncertain classification . The population is O-rich ( [ O/Fe ] \gtrsim +1.5 ) ; the light elements Na , Mg , and Al are enhanced relative to Fe in half the sample ; and for Z > 20 ( Ca ) there is little evidence for enhancements relative to solar values . These results are best explained in terms of the admixing and processing of material from H-burning and He-burning regions as achieved by nucleosynthesis in zero-heavy-element models in the literature of “ mixing and fallback ” supernovae ( SNe ) ; of rotating , massive and intermediate mass stars ; and of Type II SNe with relativistic jets . The available ( limited ) radial velocities offer little support for the C-rich stars with [ Fe/H ] < –3.1 being binary . More data are required before one could conclude that binarity is key to an understanding of this population . We suggest that the C-rich and C-normal populations result from two different gas cooling channels in the very early Universe , of material that formed the progenitors of the two populations . The first was cooling by fine-structure line transitions of C II and O I ( to form the C-rich population ) ; the second , while not well-defined ( perhaps dust-induced cooling ? ) , led to the C-normal group . In this scenario , the C-rich population contains the oldest stars currently observed .