Slice chicken breasts in half horizontally. Wrap chicken breasts in plastic wrap, and use a meat pounder to pound out until about 1/4 inch thin. Salt and pepper chicken breasts lightly.
Over medium high heat add two tablespoons of butter, and heat until the butter is bubbly. Cook chicken breasts in butter until each side is light brown. This will take about 3 or 4 minutes on each side. Remove chicken breasts when browned and set on a plate.
Add chicken broth to pan, scraping the browned bits off the pan, add the remaining butter, lemon juice, lemon zest, and capers. When sauce has reduced by 25% add chicken breasts to pan.