For the first time, three-particle interaction of protons in metallic hydrogen is studied in detail. This interaction is conditioned by the third-order member of perturbation theory for the potential of the electron—proton interaction for the energy of conduction electrons in the field of protons. As shown, the three-particle interaction of protons for the majority of protons’ configurations is small as compared with the effective pair interaction, but, for some configurations, it is much stronger than the last one. As shown, the three-particle interaction tends to compress hydrogen to higher densities than effective two-particle interaction is able to do. The maximal depth of the potential well for the three-particle interactions of protons corresponds to the location of protons in a straight line that can be interpreted as a tendency to form a cubic lattice of hydrogen in the metallic state. The crystalline state of metallic hydrogen should be stable at temperatures much higher than room one. Three-particle interaction promotes the transition of hydrogen in monoatomic state as intermediate state during the transition from molecular phase to metallic one.