Loosen skin on the top of the turkey breast, making 2 “pockets” being careful not to break the skin.
Mix the thyme and the butter and spread it on the meat under the skin.
Slice 6 thin slices off 1 orange and place 3 sliced under the skin on each side of the turkey breast. Cut up remainder of the orange and stuff it in the neck cavity. Slice the other orange in half and place under the bone side of the turkey underneath. Brush the turkey breast with the oil.
Roast for 1 1/2-2 hours or until juices run clear. If the skin is browning quickly, tent with foil for the remainder of the cooking time.