Heat the olive oil in a saute pan over medium heat. Add the chicken, skin side down, and brown well before turning to brown the meat side. When the chicken is well browned, add the onions, and cook until golden brown. Add the garlic and cook for 1 minute, add lemon juice and white wine, bring quickly to a boil, reduce heat to a low simmer, cover the pan with a tight fitting lid and cook for 5 to 8 minutes. Add 1 cup of chicken stock and continue to cook, covered, for an additional 15 minutes, or until the chicken is completely cooked. Add additional chicken stock if the pan dries out too quickly.
While the chicken is cooking, peel the carrots and place them in a saucepan with 1/4 cup water and a tablespoon butter. Season with salt and pepper and cook the carrots for 2 to 3 minutes over medium heat and set aside. Wash the asparagus and cut off any woody stem attached. Put the asparagus into a pot with 1/4 cup water and a tablespoon butter and salt and pepper. Cook over low heat for 2 minutes and set aside.
When the chicken is fully cooked, remove from the saute pan and place on a platter. Carefully ladle off any grease that has accumulated on the surface of the stock and swirl in the remaining 3 tablespoons butter to give a smooth silky finish.
Recipe courtesy of Gourmet Magazine