Preheat the oven to 425°. Remove the giblets from the chicken. Pat dry with a paper towel.

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.

Place the chicken in the oven and cook for 15 minutes. Remove from the oven and baste the chicken with the juices. Add the the grapes and garlic to the pan around the chicken. Cook, basting every 15 minutes or so, until the chicken is cooked, about 45 minutes. If the skin starts to brown too quickly, place a piece of aluminum foil loosely over the top of the chicken.

The chicken is done when it registers to 165 degrees with a meat thermometer. When fully cooked, remove the chicken, grapes, and vegetables from the cast iron and place them on a large serving platter. Cover loosely with aluminum foil to keep warm.

Set the cast iron on the stovetop. Turn heat to medium, and add the red wine. Using a wooden spoon, scrape the bottom to incorporate any browned bits. Reduce until the liquid starts to look like a sauce, about five minutes. Remove from the heat.

Serve the chicken with the roasted grapes, onions, carrots, and red wine pan gravy.