How to Make It
In a large, deep skillet, melt 2 tablespoons of the butter in the olive oil. Add the garlic. Season the chicken with salt and pepper and add to the skillet. Cook over moderately high heat until lightly browned all over, about 8 minutes. Add the vinegar and tomatoes and bring to a simmer. Cover and simmer over moderately low heat until the chicken is cooked through, about 15 minutes. Transfer the chicken to a platter and keep warm.
Boil the sauce over moderately high heat until slightly thickened, about 4 minutes. Remove from the heat.
Peel the garlic cloves and mash them into the sauce. Whisk in the remaining 2 tablespoons of butter and stir in the parsley; season with salt and pepper. Pour the sauce over the chicken and serve.