  The spin S=$\frac{1}{2}$ Kitaev honeycomb model has attracted significant
attention, since emerging candidate materials have provided a playground to
test non-Abelian anyons. The Kitaev model with higher spins has also been
theoretically studied, as it may offer another path to a quantum spin liquid.
However, a microscopic route to achieve higher spin Kitaev models in solid
state materials has not been rigorously derived. Here we present a theory of
the spin S=1 Kitaev interaction in two-dimensional edge-shared octahedral
systems. Essential ingredients are strong spin-orbit coupling in anions and
strong Hund's coupling in transition metal cations. The S=1 Kitaev and
ferromagnetic Heisenberg interactions are generated from superexchange paths.
Taking into account the antiferromagnetic Heisenberg term from direct-exchange
paths, the Kitaev interaction dominates the physics of S=1 system. Using exact
diagonalization technique, we show a finite regime of S=1 spin liquid in the
presence of the Heisenberg interaction. Candidate materials are proposed, and
generalization to higher spins is discussed.
