  In this work, we perform a combination of classical and spin wave analysis on
the one-dimensional spin-$S$ Kitaev-Heisenberg-Gamma model in the region of an
antiferromagnetic Kitaev coupling. Four phases are found, including a N\'eel
ordered phase, a phase with $O_h\rightarrow D_3$ symmetry breaking, and
"$D_3$-breaking I, II" phases which both break $D_3$ symmetries albeit in
different ways, where $O_h$ is the full octahedral group and $D_3$ is the
dihedral group of order six. The lowest-lying spin wave mass is calculated
perturbatively in the vicinity of the hidden SU(2) symmetric ferromagnetic
point.
