This is a nice, simple, and tasty classic recipe that I found in Food and Wine magazine and adapted for our own use at home. Try it out, it's sure to become a staple, and the more comfortable you get, the more you can adapt it using other flavor elements such as the veal stock option, adding mushrooms or other vegetables, or even other seasonings.
Preheat the oven to 450°. In a large, deep skillet, heat the oil. Season the chicken with salt and pepper, add to the skillet, and cook over moderately high heat until browned. Add 1 tablespoon of the butter to the skillet and swirl to coat the chicken. Turn the chicken skin side up and add the garlic and bay leaf.
Transfer the skillet to the oven and bake the chicken for 8 minutes, until the breast pieces are just white throughout. Transfer the breast pieces to a plate. Add the vinegar to the skillet, return to the oven and bake the remaining chicken, basting a few times, until cooked through, 15 minutes longer. Transfer the chicken and garlic to the plate.
Add the chicken stock and mushrooms to the skillet and boil, scraping up the browned bits, until reduced to 1 1/4 cups, about 10 minutes. Whisk in the crème fraîche and the remaining 2 tablespoons of butter. Return the chicken to the skillet along with any accumulated juices. Simmer over moderately high heat, basting a few times, until the sauce thickens slightly and the chicken is heated through about 3 minutes. Season with salt and pepper and serve.