Rinse the chicken and pat dry. Remove the giblets and set aside.
Combine the garlic, rosemary, black pepper, and sea salt and mix with 3 tablespoons of the extra-virgin olive oil. Run the outside of the chicken all over with the rosemary mixture. Place the prosciutto and cheese rinds inside the cavity, cover and refrigerate for3 hours or overnight.
Preheat the oven to 475ºF.
Place the onion slices and reserved giblets in the bottom of a small, heavy-bottomed roasting pan. Place the chicken on top of the onions, breast side up. Pour the wine over the chicken and rub all over with 1/4 cup of the vinegar. Roast in the oven for 1 hour 10 minutes, or until a skewer pushed into the thickest part of the thigh shows clear- not bloody- juices. Remove the pan from the oven and let the chicken rest for 5 minutes.
Preheat the grill or broiler.
Halve the radicchio lengthwise and grill for 3 to 4 minutes per side. Brush with the remaining olive oil and set aside.
Transfer the chicken to a carving platter and degrease the pan juices. Combine the onions and giblets with the pan juices. Carve the chicken, drizzle with the remaining 1/4 cup vinegar, and serve immediately over the radicchio. Pass the giblet gravy separately.