  We present a model based on the $SU(3)_C\otimes SU(3)_L\otimes U(1)_X$ gauge
symmetry that relates the mass hierarchy of the fermions with the solution to
the strong CP problem through the $U(1)_{PQ}$ Peccei-Quinn symmetry. This last
symmetry arises accidentally with the imposition of a discrete $Z_9$ symmetry,
which also secludes the different scales in the double seesaw mechanism taking
place in the neutrino sector. The symmetry breakdown is performed by three
scalar triplets plus a scalar singlet hosting an axion field, whose particle
excitation can be a component of dark matter. We show a mechanism where a small
effective vev is generated for a scalar triplet which is supposed to have a
bare mass above the energy scale where the $SU(3)_L\otimes U(1)_X$ symmetry is
broken. Combined with the energy scale in which the $U(1)_{PQ}$ is broken, such
a mechanism gives rise to a natural hierarchy to the fermions. Beyond the
Standard Model particle content, the model predicts an invisible axion, $a$,
three GeV neutrinos, $N_{iL}$, plus several new particles at the TeV scale
which are: five vector bosons, $U^\pm$, $V^0$, $V^{0\dagger}$, and $Z^\prime$;
one up-type $U$, and two down-type $D_a$ quarks; and at least a CP-even, $H_1$,
plus non-hermitian neutral, $\phi^0$, $\phi^{0\dagger}$, scalar bosons. The
model may be tested by looking for the possible production of such particles at
the LHC.
