We discuss the obstacles for defining a set of observable quantities analog
ous to an S-matrix which are needed to formulate string theory in an accele
rating universe. We show that the quintessence models with the equations of
state -1 < w < -1/3 have future horizons and may be no better suited to an
S-matrix or S-vector description. We also show that in a class of theories
with a stable supersymmetric vacuum, a system cannot relax into a zero-ene
rgy supersymmetric vacuum while accelerating if the evolution is dominated
by a single scalar field with a stable potential. Thus describing an eterna
lly accelerating universe may be a challenge for string theory as presently
defined.