Place the chopped onions and carrots in the middle of a large cast-iron skillet
. Carefully put the chicken on top of the carrots and onions, using the vegetables to prop the chicken off the bottom of the pan. Drizzle with chicken with the olive oil and balsamic vinegar, then sprinkle with salt and pepper all over. Stick one stalk of fresh rosemary in the cavity of the chicken. Sprinkle additional chopped rosemary on top of the chicken.