Preheat the oven to 350°. Set the chicken in a roasting pan just large enough to hold it. Sprinkle the thyme in the cavity and season the bird inside and out with salt. Tie the legs together. Pour the olive oil over the chicken and scatter the garlic cloves and peppercorns in the pan.
Roast the chicken for about 20 minutes, or until the garlic is soft and golden. Transfer the garlic to a coarse sieve set over a small saucepan. Roast the chicken for about 1 hour longer, or until the juices in the cavity run clear. Tip the chicken in the pan to drain the juices, then transfer the bird to a carving board and cover loosely with foil. Skim the fat from the pan juices and reserve 1 tablespoon. Press the garlic through the sieve into the saucepan and pour in the pan juices with the peppercorns.
In a medium skillet, heat the 1 tablespoon of reserved fat just until smoking. Add the chicken livers, season with salt and freshly ground pepper and cook over high heat until browned on both sides and pink in the center, about 1 minute. Add the livers to the pan sauce and bring the sauce to a simmer. Season with salt and remove from the heat.
Carve the chicken and arrange on plates. Spoon the sauce on top, garnish with the olives and parsley and serve.
Wine Recommendation: The 1997 Dunn Vineyards Cabernet Sauvignon and the 1999 Howell Mountain Vineyards Old Vines Zinfandel balance the luxurious flavors of the garlic and peppercorn sauce.