  We study a scenario with a transient phase of cosmological acceleration that
could potentially be realized in asymptotic corners of String Theory moduli
space. A very steep scalar potential is temporarily stabilized by the effect of
a nonzero density of heavy states, leading to acceleration, in what amounts to
a cosmological version of the Chameleon mechanism. The density of heavy states
is diluted by cosmological expansion, weakening their effect. After roughly one
$e$-fold their effect can no longer stabilize the potential, and the
accelerating phase ends. We also study a scenario where there is no potential
and the transient acceleration is achieved by the counterbalancing effects of
light and heavy towers of states. In both cases we show that it is not possible
to obtain more than $\mathcal{O}(1)$ $e$-folds without transplanckian field
excursions. We also discuss the general EFT constraints on these models and
explore a number of first attempts at concrete embeddings of the scenario in
String Theory. These all turn out to face significant challenges.
