We investigate the ability of primordial gas clouds to retain molecula
r hydrogen CPI,) during the initial phase of the reionization epoch. W
e find that before the Stromgren spheres of the individual ionizing so
urces overlap, the UV background below the ionization threshold is abl
e to penetrate large clouds and suppress their H-2 abundance. The cons
equent lack of H-2 cooling could prevent the collapse and fragmentatio
n of clouds with virial temperatures T-vir less than or similar to 10(
4) K (or masses less than or similar to 10(8) M.[(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 photoioni
zation heating.