Sprinkle chicken with salt and pepper. Heat the butter and oil in a large nonstick skillet over medium-high heat. Add chicken; cook 4 minutes on each side. Remove from pan; keep warm. Add shallots to pan; sauté 1 minute. Stir in chicken broth and vinegar, and cook 2 minutes. Add whipping cream; cook 1 minute. Serve sauce with the chicken. Sprinkle with parsley.