  We compute string scattering amplitudes in an orbifold of Minkowski space by
a boost, and show how certain divergences in the four point function are
associated with graviton exchange near the singularity. These divergences
reflect large tree-level backreaction of the gravitational field. Near the
singularity, all excitations behave like massless fields on a 1+1 dimensional
cylinder. For excitations that are chiral near the singularity, we show that
divergences are avoided and that the backreaction is milder. We discuss the
implications of this for some cosmological spacetimes. Finally, in order to
gain some intuition about what happens when backreaction is taken into account,
we study an open string rolling tachyon background as a toy model that shares
some features with R^{1,1}/Z.
