The first star formation in the Universe is expected to take place within s
mall protogalaxies, in which the gas is cooled by molecular hydrogen. Howev
er, if massive stars form within these protogalaxies, they may suppress fur
ther star formation by photodissociating the H-2. We examine the importance
of this effect by estimating the time-scale on which significant H-2 is de
stroyed. We show that photodissociation is significant in the least massive
protogalaxies, but becomes less so as the protogalactic mass increases. We
also examine the effects of photodissociation on dense clumps of gas withi
n the protogalaxy. We find that while collapse will be inhibited in low-den
sity clumps, denser ones may survive to form stars.