  An intriguing chiral soliton phase has recently been identified in the
$S$=1/2 Kitaev spin chain. Here we show that for $S$=1,2,3,4,5 an analogous
phase can be identified, but contrary to the $S$=1/2 case the chiral soliton
phases appear as islands within the sea of the polarized phase. In fact, a
small field applied in a general direction will adiabatically connect the
integer spin Kitaev chain to the polarized phase. Only at sizable intermediate
fields along symmetry directions does the soliton phase appear centered around
the special point $h^\star_x$=$h^\star_y$=$S$ where two exact product
ground-states can be identified. The large $S$ limit can be understood from a
semi-classical analysis, and variational calculations provide a detailed
picture of the $S$=1 soliton phase. Under open boundary conditions, the chain
has a single soliton in the ground-state which can be excited, leading to a
proliferation of in-gap states. In contrast, even length periodic chains
exhibit a gap above a twice degenerate ground-state. The presence of solitons
leaves a distinct imprint on the low temperature specific heat.

Strongly Correlated Electrons