Preheat oven to 400 degrees. Pat chicken dry; arrange pieces, skin side up, in a roasting pan or on a rimmed baking sheet. Season with salt and pepper. Add tangerines and olives to pan. Roast 30 minutes.
In a small bowl, whisk together tangerine juice and honey. Remove pan from oven, brush chicken with tangerine-juice mixture, and return to oven. Roast until chicken is golden and cooked through, about 10 minutes. Serve chicken with tangerines and olives.
Great Idea: Serve this dish over couscous or alongside roasted potatoes.