  We study the quasi-particle spectrum of the integrable three-state chiral
Potts chain in the massive phase by combining a numerical study of the zeroes
of associated transfer matrix eigenvalues with the exact results of the
ferromagnetic three-state Potts chain and the three-state superintegrable
chiral Potts model. We find that the spectrum is described in terms of
quasi-particles with momenta restricted only to segments of the Brillouin zone
$0\leq P \leq 2\pi$ where the boundaries of the segments depend on the chiral
angles of the model.
