Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/4-inch thickness using a meat mallet or small heavy skillet. Sprinkle chicken breasts evenly with salt and freshly ground black pepper.
Melt butter in a large nonstick skillet over medium-high heat. Place flour in a shallow dish. Dredge chicken in flour. Add chicken to pan; cook 3 minutes on each side or until done. Remove chicken from pan; keep warm. Add wine, broth, and garlic to pan, scraping pan to loosen browned bits; cook 2 minutes. Add asparagus; cover and cook 3 minutes or until asparagus is crisp-tender. Remove from heat; stir in parsley and juice. Serve asparagus and sauce with chicken.