  A central question on Kitaev materials is the effects of additional couplings
on the Kitaev model which is proposed to be a candidate for realizing
topological quantum computations. However, two spatial dimension typically
suffers the difficulty of lacking controllable approaches. In this work, using
a combination of powerful analytical and numerical methods available in one
dimension, we perform a comprehensive study on the phase diagram of a
one-dimensional version of the spin-1/2 Kitaev-Heisenberg-Gamma model in its
full parameter space. A strikingly rich phase diagram is found with nine
distinct phases, including four Luttinger liquid phases, a ferromagnetic phase,
a N\'eel ordered phase, an ordered phase of distorted-spiral spin alignments,
and two ordered phase which both break a $D_3$ symmetry albeit in different
ways, where $D_3$ is the dihedral group of order six. Our work paves the way
for studying one-dimensional Kitaev materials and may provide hints to the
physics in higher dimensional situations.
