  We investigate the ability of primordial gas clouds to retain molecular
hydrogen (H_2) during the initial phase of the reionization epoch. We find that
before the Stromgren spheres of the individual ionizing sources overlap, the UV
background below the ionization threshold is able to penetrate large clouds and
suppress their H_2 abundance. The consequent lack of H_2 cooling could prevent
the collapse and fragmentation of clouds with virial temperatures T_vir < 10^4
K (or masses 10^8 Msun [(1+z_vir)/10]^{-3/2}). This negative feedback on
structure-formation arises from the very first ionizing sources, and precedes
the feedback due to the photoionization heating.
