Place each chicken breast portion between two pieces of plastic wrap. Using the flat side of a meat mallet, pound chicken lightly until about 1/4 inch thick. Remove plastic wrap. Sprinkle with salt and pepper.
In a large skillet, melt butter over medium-high heat. Add chicken, cook 6-8 minutes or until browned and no longer pink in the center. turning once halfway through cooking. Remove chicken from pan; set aside.
Add garlic to the hot pan; cook for 30 seconds to 1 minute or until lightly browned. Add broth, scraping up any brown bits from the bottom of the pan. Bring to a boil. Add lemon slices and capers. Cover, reduce heat to low. Cook 4-5 minutes or until lemon slices are softened and releasing their juice. Return chicken to pan; heat through.
To serve, spoon caper mixture over chicken. Sprinkle with fresh parsley.