  We show that a recently proposed solution to the Hierarchy Problem
simultaneously solves the Strong CP Problem, without requiring an axion or any
further new physics. Consistency of black hole physics implies a non-trivial
relation between the number of particle species and particle masses, so that
with ~10^{32} copies of the standard model, the TeV scale is naturally
explained. At the same time, as shown here, this setup predicts a typical
expected value of the strong-CP parameter in QCD of theta ~ 10^{-9}. This
strongly motivates a more sensitive measurement of the neutron electric dipole
moment.
