Possible formation of exotic matter-antimatter molecular structure is considered as one of the most challenging problems at International Laboratories of Particle Physics. In the present work, elaborate computer codes built for investigating four-body systems are employed for calculating the binding energies of exotic molecules composed of electrons, protons, muons, pions and their antiparticles. The results confirm the stability of these molecules against dissociation to their lowest possible channels. Based on these results, it is argued that possible creation of two universes immediately after the Big Bang should be considered. Particularly, it is proposed that an overlapping area might exist between the universe and antiuniverse in which continuous creation and annihilation of simple and complicated particle-antiparticle structures might occur. Antiparticles escaping from this area are considered as the origin of the minimal traces of antiparticles appearing in our universe. Recent interpretations of cosmic-rays and gamma-radiations observed at the edge of our universe could be thought of as evidences for supporting this argument. Furthermore, it is argued that possible formation of matter-antimatter molecular structures could open the gate in front of a new field of chemistry to be referred to as Antimatter Chemistry.