3 tablespoons cold unsalted butter, cut into pieces
1 teaspoon olive oil
1/3 cup dry white wine
2 tablespoons balsamic vinegar
1 shallot, minced
1/2 cup chicken stock or canned low-sodium broth
Press half of the raspberries through a fine stainless steel strainer; reserve the puree.
Tuck one thyme sprig under the skin of each chicken breast, loosening the skin as little as possible. Season the chicken with salt and pepper.
In a large, heavy, nonreactive skillet, melt 1/2 tablespoon of the butter in the oil over high heat. When the butter stops foaming, add the chicken, skin side down, and cook for 1 minute. Reduce the heat to moderate and cook until the skin is nicely browned, about 5 minutes longer. Turn the chicken and brown the second side, about 6 minutes. Transfer the chicken to a plate and keep warm in a low oven. Pour the fat from the skillet.
Add the wine, vinegar, shallot and minced thyme to the skillet and boil over moderately high heat for 2 minutes, stirring to deglaze the pan. Add the chicken stock and boil until reduced to 1/4 cup, about 5 minutes. Stir in the reserved raspberry puree and cook until warmed through. Remove from the heat and whisk in the remaining 2 1/2 tablespoons butter.
Slice the chicken breasts crosswise or leave them whole. Transfer to warmed plates and spoon the sauce on top or alongside. Garnish with the remaining thyme sprigs and whole raspberries and serve.