Rinse chicken and pat dry; cut into 1 1/2- to 2-inch pieces. Pour olive oil into a 10- to 12-inch frying pan over medium-high heat; when hot, add chicken and turn pieces often to brown on all sides, 5 to 8 minutes total. With a slotted spoon, transfer chicken to a bowl.
Add butter to pan; when melted, add onions and garlic and stir often until onions are limp and beginning to brown, 5 to 7 minutes. Return chicken to pan and spread level. Sprinkle cumin, ginger, cinnamon, turmeric, paprika, 1/2 teaspoon salt, dark and golden raisins, and pistachios over chicken. Add preserved lemons if using. Pour 1 cup broth evenly over all. Cover and bring to a boil, then reduce heat and simmer, stirring occasionally, until chicken is no longer pink in the center (cut to test), 5 to 6 minutes.
Meanwhile, in a 3- to 4-quart pan over high heat, bring 1 1/2 cups water to a boil; stir in couscous and return to a boil. Cover pan, remove from heat, and let stand until water is absorbed, about 5 minutes. Fluff couscous with a fork and stir in mint.
Scoop couscous equally onto dinner plates or into wide bowls. If chicken tagine is drier than desired, thin with more broth. Spoon over couscous and sprinkle with cilantro. Add salt and pepper to taste.