Preheat oven to 450 degrees. Pour oil into large roasting pan. Add chicken, onion, and mushrooms, turning to coat with oil. Bake 5 minutes; turn chicken over and stir vegetables. Bake an additional 5 minutes.
Meanwhile, in medium bowl, whisk flour into chicken broth. Add vinegar, lemon juice, salt and pepper, stirring well.
When chicken has cooked for 10 minutes, add broth mixture to roasting pan. Cover with foil and bake 10 minutes. Remove foil, stir vegetables, and bake, uncovered, until sauce bubbles and is slightly thickened, about 10 minutes.
Heat broiler. Turn chicken over. Place pan 6 inches from heat and broil until chicken just starts to turn golden, about 3-5 minutes. Serve immediately.
Variation: Reduce chicken broth to 1/2 cup, delete the vinegar, and add 3/4 cup Marsala wine.