We propose and examine a new high-density composite of Λ * ≡ K − p = (sū) ⊗ (uud), which may be called Kaonic Proton Matter (KPM), or simply, Λ * -Matter, where substantial shrinkage of baryonic bound systems originating from the strong attraction of the (KN ) I=0 interaction takes place, providing a ground-state neutral baryonic system with a huge energy gap. The mass of an ensemble of (K − p)m, where m, the number of the K − p pair, is larger than m ≈ 10, is predicted to drop down below its corresponding neutron ensemble, (n)m, since the attractive interaction is further increased by the Heitler-London type molecular covalency, as well as by chiral symmetry restoration of the QCD vacuum. Since the seed clusters (K − p, K − pp and K − K − pp) are short-lived, the formation of such a stabilized relic ensemble, (K − p)m, may be conceived during the Big-Bang Quark Gluon Plasma (QGP) period in the early universe before the hadronization and quark-antiquark annihilation proceed. At the final stage of baryogenesis a substantial amount of primordial (ū,d)'s are transferred and captured into KPM, where the anti-quarks find places to survive forever. The expected KPM state may be cold, dense and neutralqq-hybrid (Quark Gluon Bound (QGB)) states, [s(ū ⊗ u)ud]m, to which the relic of the disappearing anti-quarks plays an essential role as hidden components. Explosive production of KPM from supernova precursors is considered as a possible observational astronomical process.PACS numbers: