  We consider the possibility of gauge coupling unification within the simplest
realizations of the $\mathrm{SU(3)_c \times SU(3)_L \times SU(3)_R \times
U(1)_{X}}$ gauge theory. We present a first exploration of the renormalization
group equations governing the "bottom-up" evolution of the gauge couplings in a
generic model with free normalization for the generators. Interestingly, we
find that for a $\mathrm{SU(3)_c \times SU(3)_L \times SU(3)_R \times
U(1)_{X}}$ symmetry breaking scale $M_X$ as low as a few TeV one can achieve
unification in the presence of leptonic octets. We briefly comment on possible
grand unified theory frameworks which can embed the $\mathrm{SU(3)_c \times
SU(3)_L \times SU(3)_R \times U(1)_{X}}$ model as well as possible
implications, such as lepton flavour violating physics at the LHC.
