  The evolution of a gas shell, swept by the supernova remnant of a massive
first generation star, is studied with H_2 and HD chemistry taken into account.
When a first-generation star explodes as a supernova, H_2 and HD molecules are
formed in the swept gas shell and effectively cool the gas shell to
temperatures of 32 K - 154 K. If the supernova remnant can sweep to gather the
ambient gas, the gas shell comes to be dominated by its self-gravity, and
hence, is expected to fragment. Our result shows that for a reasonable range of
temperatures (200 K - 1000 K) of interstellar gas, the formation of
second-generation stars can be triggered by a single supernova or hypernova.
