  An orthogonal basis of the Hilbert space for the quantum spin chain
associated with the su(3) algebra is introduced. Such kind of basis could be
treated as a nested generalization of separation of variables (SoV) basis for
high-rank quantum integrable models. It is found that all the monodromy-matrix
elements acting on a basis vector take simple forms. With the help of the
basis, we construct eigenstates of the su(3) inhomogeneous spin torus (the
trigonometric su(3) spin chain with antiperiodic boundary condition) from its
spectrum obtained via the off-diagonal Bethe Ansatz (ODBA). Based on small
sites (i.e. N=2) check, it is conjectured that the homogeneous limit of the
eigenstates exists, which gives rise to the corresponding eigenstates of the
homogenous model.
