Mix garlic, ginger, paprika, cumin, pepper, and oil in a bowl. Ease fingers under chicken skin to loosen. Add chicken to bowl; rub garlic mixture under skin and all over outside. Chill, covered, overnight.
Preheat oven to 500°. In a small bowl, combine saffron with 2 tbsp. hot water and let sit 5 minutes. Set chicken, skin side up, in a deep 10-in. or regular 12-in. ovenproof frying pan. In same bowl used for chicken, combine onion, olives, and preserved lemon; put on top of chicken. Combine broth, saffron water, and turmeric in bowl and pour over chicken. Cover tightly with foil.
Braise chicken in oven, turning in sauce every 20 minutes, until tender when pierced, 60 to 70 minutes. Skim fat from sauce. Sprinkle chicken with cilantro and serve with couscous.
*Find Lucques olives at well-stocked grocery stores. To pit, set on a work surface, set flat side of a wide knife on top, then smack with your hand and pick out the pits. Find preserved lemons at well-stocked grocery stores or robertlambert.com.