Currently, neutron matter and neutron stars as subjects of research are firmly established in physics and astrophysics. It is logical to consider their chemical properties, based on the principles of general chemistry. The paper shows how neutron matter is formed; besides gravitational neutronization, other mechanisms, such as condensation of ultracold neutrons (UCN) and neutronization by critically increasing the sequence number of elements in the Periodic System (PS) are considered. Thus, arises the question of a possible “end” of the PS. Proceeding from the initial D.I. Mendeleev’s premise concerning his PS, the neutron matter must inevitably be placed in a group of rare gases and at the “beginning” of the System. The possibility of a chemical interaction of UCN with the substances with an odd number of electrons is also considered. A planned experiment to study the chemical properties of UCN is discussed. We offer to expand PS beyond classical chemical substances and use it to cover much wider universe matter, based on the forgotten ideas of D.I. Mendeleev. As a result, neutron and its isotopes (dineutron, tetraneutron, etc.) will begin and the neutron star matter will end the PS.