In a medium pot, heat a drizzle of oil over medium-high heat and saute the onion for 4-5 minutes, until soft. Squeeze the sausage out of its casing into the pan and cook it, breaking it up with a spoon, until it's no longer pink. Add the garlic and chili powder and cook for another minute or two.
Add the chicken stock and stir to loosen any browned bits from the bottom of the pan. Add the squash and bring to a simmer; cook for 20-30 minutes, until the squash is tender. Stir in the beans. (Alternatively, toss the lot into a slow cooker and turn it on low for 8 hours.)
In a small skillet, heat the butter over medium-high heat and saute the apple for a few minutes, turning until golden and caramelized. Stir into the chili before serving.