Preheat the oven to 350F. Arrange the squash halves, cut-side down, on a baking sheet and bake until soft (about 30 minutes).
Season the chicken breasts with salt and pepper and bake along-side the squash until cooked (about 30 minutes).
While the squash is cooking, heat the oil in a large skillet over medium heat. Stir in the carrots and celery and saute until soft (about 5 minutes), then add the garlic and cook for an additional minute.
Once the squash and chicken are ready, remove them from the oven and flip the squash.
Combine the brown sugar and melted butter and brush over the squash. Cover to keep warm.
Dice the chicken to add to the mixture.
Stir the garbanzo beans, chicken and raisins into the mixture and season the mixture with the cumin, salt and pepper. Continue to cook until heated through and vegetables are tender (about 3 minutes).
Pour the chicken broth into a separate saucepan and cook the quinoa until all of the broth is absorbed and quinoa is tender (about 10 minutes).
Combine the quinoa and chicken mixture and spoon into each squash halve.
Serve with additional filling if desired.
This recipe makes about 1 1/2 cups of extra filling. It can be served alongside the filled squash or 1 additional squash can be cooked to serve 2 additional people.