Champagne and mushrooms lends this dish delicate flavor, but you could use white wine also. Ask your butcher to bone the chicken breasts, which offer the best results, or use skinned and boned breasts.
Stir together first 3 ingredients in a shallow bowl. Dredge chicken in flour mixture; place on a wire rack. Let stand 15 minutes. Dredge chicken in flour mixture again; return to rack.
Melt butter with olive oil in a large skillet over medium heat. Cook chicken, in batches, 5 minutes on each side or until golden brown. Remove chicken to a plate.
Add shallots to skillet; cook, stirring often, 2 minutes or until golden brown. Add mushrooms and garlic, and cook, stirring often, 10 minutes or until mushrooms are tender. Stir in Champagne and thyme; bring to a boil, stirring to loosen browned particles from bottom of skillet. Reduce heat, and return chicken to skillet. Cover and simmer 10 minutes or until done.
Transfer chicken to a serving platter. Stir cream into mushroom mixture. Cook 5 to 6 minutes or until thickened. Add salt and pepper to taste. Serve sauce immediately over chicken.
I love this dish and have made it on a few occasions and everyone loved it!