  We argue that the Nelson-Barr solution to the Strong CP Problem can be
naturally realized in an E$_6$ Grand-Unified Theory. The chiral SM fermions
reside in three generations of E$_6$ fundamentals together with heavy
vectorlike down quarks, leptons doublets and right-handed neutrinos. CP is
imposed on the Lagrangian and broken only spontaneously at high scales, leading
to a mixing between chiral and vectorlike fields that allows to solve the
Strong CP Problem through the Nelson-Barr mechanism. The main benefit of the
E$_6$ GUT structure is the predictivity in the SM fermion sector, and a perfect
fit to all SM observables can be obtained despite being over-constrained.
Definite predictions are made for the neutrino sector, with a Dirac CP phase
that is correlated to the CKM phase, allowing to test this model in the near
future.
