Cut each chicken breast in half horizontally. Place each 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 chicken with salt and pepper.
In a large skillet, melt butter over medium-high heat. Add chicken; cook for 6-8 minutes or until browned and no longer pink in center, turning once halfway through cooking. Remove chicken from skillet; set aside.
Add garlic to the hot skillet; cook for 30 seconds to 1 minute or until lightly browned. Add chicken broth to skillet, scraping up any browned bits from the bottom of the skillet. Bring to boiling. Add lemon slices and capers. Cover; reduce heat to low. Cook for 4 to 5 minutes or until lemon slices are softened and releasing their juice. Return chicken to skillet; heat through.
To serve, spoon caper mixture over chicken. Sprinkle with fresh parsley.