We use one-dimensional radiative transfer simulations to study the evolutio
n of H-2 gas-phase (H- catalyzed) formation and photodissociation regions i
n the primordial universe. We find a new positive feedback mechanism capabl
e of producing shells of H-2 in the intergalactic medium (IGM), which are o
ptically thick in some Lyman-Werner bands. While these shells exist, this f
eedback effect is important in reducing the H-2 dissociating background flu
x and the size of photodissociation spheres around each luminous object. Th
e maximum background opacity of the IGM in the H-2 Lyman-Werner bands is ta
u (H 2)approximate to1-2 for a relic molecular fraction chi (H 2)=2x10-6, a
bout 6 times greater than that found by Haiman, Abel, & Rees. Therefore, th
e relic molecular hydrogen can decrease the photodissociation rate by about
an order of magnitude. The problem is relevant to the formation of small p
rimordial galaxies with masses M(DM)less than or similar to 10(8) M-circle
dot that rely on molecular hydrogen cooling to collapse. Alternatively, the
universe may have remained dark for several hundred million years after th
e birth of the first stars, until galaxies with virial temperature T(vir)gr
eater than or similar to 10(4) K formed.