Place chicken breasts between two sheets of saran wrap. Pound out to 1/2" thickness. If desired, you may cut the breasts into smaller portions (depending on the size, mine were huge).
Season with salt and pepper, then dredge with flour.
In a skillet over medium high heat, melt together 1 T olive oil with 2 T butter.
When the pan is hot, add the chicken breasts. Saute chicken chicken until browned and cooked through, 3-4 minutes per side.
Add the chicken broth, lemon juice and capers to the pan, scraping up any browned bits from the bottom of the pan. Turn chicken so both sides are coated in sauce. Simmer until slightly reduced (1 minute); whisk in 1 T butter. Serve chicken topped with sauce; sprinkle with parsley.