  Non-trivial inflaton self-interactions can yield calculable signatures of
primordial non-Gaussianity that are measurable in cosmic surveys. Surprisingly,
we find that the phase transition to slow-roll eternal inflation is often
incalculable in the same models. Instead, this transition is sensitive to the
non-Gaussian tail of the distribution of scalar fluctuations, which probes
physics inside the horizon, potentially beyond the cutoff scale of the
Effective Field Theory of Inflation. We demonstrate this fact directly by
calculating non-Gaussian corrections to Stochastic Inflation within the
framework of Soft de Sitter Effective Theory, from which we derive the
associated probability distribution for the scalar fluctuations. We find
parameter space consistent with current observations and weak coupling at
horizon crossing in which the large fluctuations relevant for eternal inflation
can only be determined by appealing to a UV completion. We also show this
breakdown of the perturbative description is required for the de Sitter entropy
to reflect the number of de Sitter microstates.
