  We propose a technically natural scenario whereby an initially large
cosmological constant (c.c.) is relaxed down to the observed value due to the
dynamics of a scalar evolving on a very shallow potential. The model crucially
relies on a sector that violates the null energy condition (NEC) and gets
activated only when the Hubble rate becomes sufficiently small --- of the order
of the present one. As a result of NEC violation, this low-energy universe
evolves into inflation, followed by reheating and the standard Big Bang
cosmology. The symmetries of the theory force the c.c. to be the same before
and after the NEC-violating phase, so that a late-time observer sees an
effective c.c. of the correct magnitude. Importantly, our model allows neither
for eternal inflation nor for a set of possible values of dark energy, the
latter fixed by the parameters of the theory.
