Recently, Fall and Rees (1985) have proposed a theory for the origin of globular clusters forming from the largely primordial gas in the protogalaxy. These authors have explained the typical masses of proto-globular cluster clouds (~ 106 M⊙) as gravitationally unstable condensations at temperature T ~ 104 in a hot protogalactic medium (T ~ 106 K) but they were not concerned with how these clouds would fragment into stellar masses (~ 1 M⊙). In fact, their proto-globular cluster clouds are trapped at T ~ 104 K, and cannot cool to lower temperatures. However, substantial cooling must occur if these clouds are to form solar mass stars. It is known that under primordial conditions the only available cooling agent is molecular hydrogen, formed in the gas phase. Therefore, if sufficient molecular hydrogen is formed, it is possible to cool the gas well below T ~ 104 K. In the following we outline how non-equilibrium conditions lead to a larger H2 abundance than derived by Fall and Rees, who assumed equilibrium conditions.