Put oil and butter in a large skillet or casserole, which can be covered later, and turn heat to medium high. When butter melts, add onion, and cook, stirring occasionally, until it softens, 5 to 10 minutes. Add garlic, a large pinch of salt and spices. Cook, stirring, for about 30 seconds. Add tomatoes, chickpeas, raisins and vanilla, and bring to a boil. (If mixture is very dry, add about 1/2 cup water.) Taste, and add salt as necessary.
Sprinkle chicken pieces with salt, and nestle them into sauce. Cover, and 5 minutes later adjust heat so mixture simmers steadily. Cook until chicken is very tender, 45 minutes to an hour. Taste, and adjust seasoning. Then garnish, and serve with couscous.