Heat a large high sided skillet, or dutch oven, over medium high heat. Add the chicken, tossing with the oil. Season with salt & pepper, to taste, and cook until the chicken's cooked through. Remove the chicken from the pan, and set aside.
Add the mushrooms & onion to the pan, tossing with the last tablespoon of oil. Stirring occasionally, cook until the mushrooms are done.
Add the chicken, broth, cream, wine, and pasta back to the skillet. Bring the mixture to a boil, reduce to a slow simmer and cover.
Continue simmering, stirring occasionally, for 15-20 minutes or until the pasta is cooked through.
Remove the skillet from heat, stir in the cheese, and serve immediately.