Heat the chicken stock in a small saucepan over medium-high heat. Add the barley and simmer until tender, about 8 to 10 minutes.
Scoop the seeds from each squash half and place, cut sides up, in a microwave-safe baking dish. Cover loosely with plastic wrap and microwave on high for 5 minutes, or until flesh is tender.
Meanwhile, heat the oil in a large saucepan over medium heat. Add chicken, onion, green pepper and saute 3 minutes. Add sage, salt and pepper, to taste, and cooked barley and stir to coat. Cook, stirring constantly, until chicken is cooked through and mixture is well-combined.
Spoon barley mixture into each halved squash. Transfer stuffed squash to a foil-lined baking sheet or a baking dish and top with goat cheese. Bake for 5 to 7 minutes, or until cheese is lightly browned.