In a small bowl, combine 3 tablespoons of the thyme with 1 1/2 teaspoons of salt and the garlic, fennel and allspice. Sprinkle the mixture all over the chicken and place in a deep casserole. Cover and refrigerate overnight.
Preheat the oven to 275°. Pour the pure olive oil over the chicken and bake for about 2 hours, until tender. Using tongs, transfer the chicken to a rack set over a baking sheet and let drain for 20 minutes; reserve 2 tablespoons of the confit oil.
Meanwhile, increase the oven temperature to 400°. Spoon 1 tablespoon of the confit oil into a medium saucepan. Add the onion and carrot and cook over moderate heat, stirring occasionally, until softened, about 7 minutes. Add the couscous and stir to coat with oil. Add the water and a generous pinch of salt and bring to a boil. Cover and remove from the heat. Let stand until the couscous is tender and plumped, about 10 minutes. Fluff with a fork, cover and keep warm.
Press the chicken legs slightly to flatten them. In a large, ovenproof nonstick skillet, heat the remaining 1 tablespoon of confit oil. Add the chicken, skin side down, and cook over moderately high heat until the skin begins to crisp, about 3 minutes. Transfer the skillet to the oven and roast the chicken for about 8 minutes, until heated through and the skin is very crisp.
Meanwhile, in a small bowl, whisk the lemon zest and juice with the remaining 1/2 tablespoon of thyme and the extra-virgin olive oil. Stir in the olives and mint and season with salt and pepper. Spoon the couscous onto plates and top with the chicken legs. Spoon the dressing over the chicken and couscous and serve right away.