Preheat the oven to 350°. In a skillet, melt the butter. Add the squash, cover and cook over moderate heat until almost tender, 3 minutes. Add the shallot and cook for 1 minute. Add the apple, cinnamon and cayenne and cook for 1 minute. Add the raisins, wine, honey and thyme and cook until the wine is almost evaporated. Season with salt and pepper.
In an ovenproof nonstick skillet, heat the oil. Season the chicken with salt and pepper and add to the skillet, skin side down. Cook over high heat until the skin is crisp, 5 minutes. Turn the chicken, transfer the skillet to the oven and roast for 6 minutes, until cooked through; serve with the compote.