In contrast to the bulk MoS2, the structure of the active phase of the catalyst prepared via exfoliation is shown to exhibit a number of distortions, which form a superstructure of the type of the charge density waves with a quasi-period of 30 Angstrom. Due to such distortions, the ions of cobalt firmly chemisorb on the basal plane of MoS2 occupying, along the perimeter of the MoS2 clusters, the regions with a lower energy of the Mo-S interaction. A synergetic increase in the catalyst activity due to the introduction of cobalt was observed up to the atomic ratios of Co/(Co+Mo) = 0.33, which is possible for the nanoparticles of MoS2 with a diameter 200 Angstrom, only if cobalt adsorbs on the basal plane.