The chemical and thermal evolution of the baryon component in the gravitational field of low-mass primordial dark-matter halos during their virialization is studied. We consider low-mass halos to be those for which the characteristic baryon cooling time can appreciably exceed the comoving Hubble time, so that the cooling process can continue to the current epoch (z∼0). The virialization process is described in two scenarios: “quiet” virialization, in which the establishment of the virial state is assumed to be homogeneous over the entire volume considered, and “violent” virialization, in which the establishment of the virial state is assumed to be realized via the action of shock waves. In this second case, the efficiency of the formation of molecular hydrogen grows substantially, and can reach H2/H∼0.01 in some cases, which exceeds current estimates by at least an order of magnitude. This eases the condition for the birth of the first gravitationally bound objects with comparatively low masses (M ≳ 2 × 105M⊙), possibly leading to an appreciable increase in the fraction of the mass contained in Population III objects, and also to a shift in the onset of the formation of the first stars toward higher redshifts.