Heat oven to 450 degrees F and arrange rack in middle.
In a large bowl, mix together 1/4 cup of the oil, rosemary, salt, red pepper flakes, and freshly ground black pepper. Add chicken pieces and turn to coat well. Slip 1 piece of orange under skin of each piece.
Heat remaining 1 tablespoon olive oil and butter in a cast iron skillet or large frying pan over medium-high heat until butter foams. Working in batches, add 3 or 4 chicken pieces (don't overcrowd the pan) and brown on both sides until skin is crisp and golden, about 2 to 3 minutes per batch. As chicken is finished, place in a 13 by 9-inch baking dish.
Once all chicken has browned, place in oven to roast until juices run clear when pricked with a knife and meat registers 160 to 165 degrees F on an instant-read thermometer, about 20 to 25 minutes. Let rest 5 minutes before serving.
Recipe courtesy of Aida Mollenkamp