In a large non-stick skillet over medium heat, heat 1 tablespoon of the oil, and cook the onions until tender, about 5 minutes. Add the mushrooms and cook until softened, about 5 minutes. Remove to a plate and cover to keep warm.
In the same skillet, heat the remaining oil, and sauté chicken strips until cooked through, about 4 to 5 minutes.
Return the onion and mushroom mixture to the skillet with the chicken and add salt and pepper. Stir in the sour cream, stirring well to mix, and cook until the mixture is well heated through, about 3 minutes.