Unless you are using a couscousiere, combine chicken, oil, butter, onionn, tomato, pepper, cinnamon stick, and salt in a large, heavy pot. Stir over medium heat to coat and brown the chicken. After about 5 minutes, cover with 1 1/2 cups water and bring to a boil. Toss in the chickpeas, then simmer, covered, 30-40 minutes until chicken is tender. Remove the chicken pieces and set them aside.
Continue to cook the mixture in the pot until chickpeas are tender, perhaps another 1 1/2 hours. Add more water if necessary, to retain roughly the same level. When chickpeas are done, return the chickpeas to the pot to heat through. To serve in a traditional manner, distribute the couscous in a large bowl or platter with curved edges, and ladle on as much liquid from the as the couscous will absorb. Pile chicken in the center, and finish by ladling chickpeas and sauce over all.