For the Marinade: Bring ingredients to a boil in a medium saucepan and reduce to 2 cups and let cool.
For the Chicken: Place chicken in a large baking dish. Brush 1 cup of the marinade over the chicken and inside the cavity. Cover and marinate in the refrigerator for at least 4 hours or up to 8 hours. Preheat oven to 450 degrees F. Remove the chicken from the marinade and place the oranges, garlic and onions in the cavity and truss. Season well with salt and coarsely ground black pepper. Brush with more of the marinade. Place the chicken in a medium roasting pan and roast in the oven for 15 minutes. Turn the heat down to 375 degrees and continue roasting for 1 to 1 1/4 hours, basting with the marinade every 15 minutes. Remove the chicken to a cutting board and let rest 10 minutes. Degrease the pan and place the roasting dish with the drippings on top of 2 burners over high heat. Add the wine and orange juice and reduce by half. Add the chicken stock and reduce by half. Swirl in the butter and add the chives. Season with salt and pepper to taste.
For the Polenta: Heat oil and butter in a large saute pan over high heat. Add the shallots and cook until soft. Add the mushrooms and cook until golden brown. Add the wine and cook until completely reduced. Season with salt and pepper and fold in the thyme and parsley, set aside. Heat a small saute pan over high heat. Add the polenta and toast until lightly golden brown. Bring water to a boil in a large saucepan and add 1 tablespoon of salt. Slowly whisk in the toasted polenta, and reduce the heat to low. Switch to a wooden spoon and continue cooking until the mixture begins to pull away from the pan. Add the mushrooms, cheese and season with salt and pepper. If the mixture is too thick, add more water.