Remove the backbone and wings from the chicken. Press the chicken open like a book. Carefully remove the bones from the chicken leaving the whole chicken intact with the skin. You can ask your butcher to do this for you.
In a small bowl, combine the goat cheese, rosemary, and olive oil. Season with salt and pepper and mash together with the back of a fork.
Turn the chicken over so the skin side is up. Gently loosen the skin by inserting your fingers underneath it to make a pocket. Stuff the rosemary goat cheese under the skin evenly over the breasts and legs. Tuck the skin back over the chicken. Season both sides of the chicken well with salt and pepper. Drizzle a little olive oil over the chicken and rub well.
Heat a large, ovenproof saute pan over high heat. When the pan is hot, add enough olive oil to coat the bottom of the pan. When the oil is hot and begins to shimmer when swirled, add the chicken, skin side down. Cook the chicken until the skin side is a deep golden brown, about 8 to 10 minutes. Carefully turn the chicken over and transfer to the oven. Roast for 10 minutes, or until the chicken is cooked through and the juices run clear.
Remove the chicken from the pan and keep warm. Remove all but 2 tablespoons of the fat from the pan and return to the heat. Add 1 tablespoon of the butter and the shallots and saute for 2 minutes, scraping the bottom of the pan with a wooden spoon to loosen the browned bits. Add the mushrooms and season with salt and pepper. Saute for 2 minutes, or until the mushrooms begin to brown. Add the stock and bring to a simmer. Cook 5 minutes or until reduced by 1/3. Stir in the remaining tablespoon of butter and remove from the heat. Pour the sauce over the chicken and garnish with the chives. Serve immediately.