In a food processor blend the garlic, onion, tangerine zest and juice, honey, rosemary, and olives with broth and salt and pepper.
Marinate the chicken with the olive mixture and set chicken pieces in an oiled baking dish. Scatter with chopped figs and tangerine wedges, tucking them between the pieces of chicken.
Place chicken in oven and roast until completely cooked through, reaching an internal temperature of 165°F, about 40 minutes, until browned and caramelized. This can be served directly from the baking dish or transfer onto a serving platter, spooning juices over top of the chicken.