Melt 4 tablespoons of the butter in a medium saucepan over moderate heat. Saute the onions with 1/2 teaspoon each of salt and pepper until golden brown, 8 to 10 minutes. Add the garlic and half of each of the mushrooms. Turn up the heat and cook the mushrooms, stirring frequently, until golden. Pour in the wine and cook until most of the liquid has evaporated.
Meanwhile, place the Ancho chiles over a burner and toast all over just until soft and the skin is slightly bubbly. Roughly chop half the chiles and add to the pot, reserving the rest.
Add the chicken stock to the pot and boil about 12 minutes. Transfer to a blender or food processor and puree until smooth. (For a smoother sauce, pass through a sieve.) Return the sauce to the stove and bring to a boil. Stir in the remaining butter, 1 tablespoon at a time, and remove from heat. (For a thinner, more rustic sauce you can eliminate this butter.) Stir in the lime juice, season with salt and pepper and reserve.
Preheat the oven to 350 degrees.
Season the chicken breasts well with salt and pepper. Heat a large dry skillet over moderate heat for 5 minutes. Pour in the olive oil and place the chicken in the pan, skin side down. Fry until the skin starts to brown and crisp, 5 to 10 minutes, and then turn and briefly sear the other side. Transfer to a baking dish (set the pan aside) and bake until cooked through, about 10 minutes.
Meanwhile, finish the sauce by thinly slicing the remaining toasted Ancho peppers. Reheat the pan used to brown the chicken and saute the remaining mushrooms over medium-high heat until the edges are brown. Then add the sliced Anchos. Stir and toss 1 to 2 minutes longer. Stir into the reserved sauce.
Coat the serving plates with the sauce. Top each with a browned chicken breast and serve.
c.1996, M.S. Milliken & S. Feniger, all rights reserved