  The approximate conservation of $CP$ can be naturally understood if it arises
as an automatic symmetry of the renormalizable Lagrangian. We present a
specific realistic example with this feature. In this example, the global
Peccei-Quinn symmetry and gauge symmetries of the model make the renormalizable
Lagrangian $CP$ invariant but allow non zero hierarchical masses and mixing
among the three generations. The left-right and a horizontal $U(1)_H$ symmetry
is imposed to achieve this. The non-renormalizable interactions invariant under
these symmetries violate $CP$ whose magnitude can be in the experimentally
required range if $U(1)_H$ is broken at very high, typically, near the grand
unification scale.
