We propose a novel scenario to explain the observed cosmological asymmetry between matter and antimatter, based on nonperturbative QCD physics. This scenario relies on a mechanism of separation of quarks and antiquarks in two coexisting phases at the end of the cosmological QCD phase transition: ordinary hadrons (and antihadrons), along with massive lumps (and antilumps) of novel color superconducting phase. The latter would serve as the cosmological cold dark matter. In certain conditions the separation of charge is C and CP asymmetric and can leave a net excess of hadrons over antihadrons in the conventional phase, even if the visible universe is globally baryon symmetric $B = 0$. In this case an equal, but negative, overall baryon charge must be hidden in the lumps of novel phase. Due to the small volume occupied by these dense lumps/antilumps of color superconducting phase and the specific features of their interaction with "normal" matter in hadronic phase, this scenario does not contradict the current phenomenological constrains on presence of antimatter in the visible universe. Moreover, in this scenario the observed cosmological ratio $Ω_{DM}\simΩ_{B}$ within an order of magnitude finds a natural explanation, as both contributions to $Ω$ originated from the same physics during the QCD phase transition. The baryon to entropy ratio $n_{B}/n_γ\sim 10^{-10}$ would also be a natural outcome, fixed by the temperature $T_f \simlt T_{QCD}$ at which the separation of phases is completed.

New paragraph added in subsection II.D; version to appear in Physical Review D