Rub 1 teaspoon of coconut oil onto each half of the squash. Sprinkle with 1 tablespoon of coconut sugar. Bake until the acorn squash, flesh side up, until tender, about 30 - 40 minutes.
While the squash is cooking, prepare the chicken and quinoa. If you're not using leftover chicken, either grill or pan-sear the chicken as you would normally. For the quinoa, add the quinoa and water to a saucepan and bring to a boil. Cover and reduce to a simmer for 10 - 15 minutes. Remove from the heat, and keep covered for 5 minutes. Fluff with a fork and set aside.
Heat the olive oil in a skillet over medium heat. Add the kale and cook until it's started to wilt, add the chicken and quinoa and toss to combine. Season with spices and remove from the heat.
Remove the squash from the oven, and let cool for a few minutes. Transfer to two plates and stuff with half the chicken-quinoa mixture.