To Marinate: Pour 1/2 of the beer into a nonporous glass dish or bowl. Add chicken breasts, toss to coat, cover dish and refrigerate for 30 minutes to marinate.
Melt 1 tablespoon of the butter in a large skillet over medium heat. Add mushrooms and saute for 5 to 10 minutes or until cooked; remove from skillet and reserve, keeping warm.
Melt remaining 1 tablespoon butter in skillet over medium high heat and add chicken. Saute 5 to 6 minutes each side or until cooked through and juices run clear. Reduce heat to low, pour remaining beer over chicken and add reserved mushrooms. Cover skillet and let simmer for 5 to 10 minutes. Sprinkle with cheese and serve.