Preheat oven to 300 degrees F.
In a small roasting pan, mix together the olives, rosemary, chile, and garlic. Slice the tangerines in half and squeeze the juice over the olives; toss in the rinds. Pour over the olive oil and vinegar and give it a good stir. Cover with foil and bake for about 1 hour. Serve warm or at room temperature.