  Thermal and chemical evolution of primordial gas clouds irradiated with
far-ultraviolet (FUV; < 13.6 eV) radiation is investigated. In clouds
irradiated by intense FUV radiation, sufficient hydrogen molecules to be
important for cooling are never formed. However, even without molecular
hydrogen, if the clouds are massive enough, they start collapsing via atomic
hydrogen line cooling. Such clouds continue to collapse almost isothermally
owing to successive cooling by H^{-} free-bound emission up to the number
density of 10^{16} cm^{-3}. Inside the clouds, the Jeans mass eventually falls
well below a solar mass. This indicates that hydrogen molecules are dispensable
for low-mass primordial star formation, provided fragmentation of the clouds
occurs at sufficiently high density.
