Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Place 1 chicken breast half in a large heavy-duty zip-top plastic bag; pound to a 1/4-inch thickness. Repeat procedure with remaining chicken. Sprinkle chicken evenly with salt and pepper. Add chicken to pan; cook 3 minutes on each side or until done. Remove from pan; keep warm.
Heat 1 teaspoon of oil in pan over medium-high heat. Add mushrooms, garlic, thyme, and asparagus; cook 3 minutes, stirring frequently. Combine broth and cornstarch, stirring with a whisk. Add broth mixture, vinegar, and juice to pan; bring to a boil. Cook 1 minute or until slightly thick. Serve over chicken.