We study the formation of molecular hydrogen in cooling gas behind sho
cks produced during the blow-away process thought to occur in the firs
t collapsed, luminous (Population III) objects in the early universe.
We find that for a wide range of physical parameters, the H-2 fraction
is f approximate to 6 x 10(-3). The H, mass produced in such explosio
ns can exceed the amount of relic H-2 destroyed inside the photodissoc
iation region surrounding a given Population III object. We conclude,
differently from the suggestion of Haiman et al., that these first obj
ects might have a net positive feedback on subsequent galactic formati
on. We discuss the effects of radiation and the implications of our re
sults for the soft-UV background.