Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/2-inch thickness using a meat mallet or rolling pin.
Sprinkle chicken with salt, pepper, and flour.
Heat 1 tablespoon butter in a large nonstick skillet over medium heat.
Add chicken; cook 5 minutes on each side or until done.
Remove chicken from pan; keep warm.
Add mushrooms and shallots to pan; saut 5 minutes or until tender. Stir in wine, scraping pan to loosen browned bits; add stock. Bring to a boil; cook until reduced to 1 cup (about 10 minutes).
Cut remaining 1 tablespoon butter into small pieces.
Remove pan from heat.
Add butter, stirring until butter melts. Spoon sauce over chicken.