Using a meat tenderizer hammer, pound butterflied chicken breasts so they are even in thickness. I like to put plastic wrap in between the chicken and the hammer. Season chicken with salt and pepper. Dredge chicken in flour to coat all over, and shake off excess. Set aside on a plate.
Melt 2 tbsp of butter, and 2 tbsp olive oil in a large skillet over med-high heat. When it starts to sizzle add 2 of the 4 chicken breasts and cook for about 3 minutes. Once browned, flip and cook for another 3 minutes. Remove from pan onto a plate. Melt 2 more tbsp of butter, and another 2 tbsp of olive oil. Add the remaining 2 chicken breast and repeat cooking instructions. Remove from pan once cooked.
In the skillet (chicken removed) add the lemon juice, stock, and capers. Bring to a boil scraping the brown chicken bits from the pan, they add great flavor! Salt and pepper sauce if needed. Return all of the chicken to the pan and simmer over medium heat for about 5 minutes.
Remove chicken onto a serving platter. Add 2 more tbsp of butter to the skillet and whisk quickly. Serve sauce over chicken. Garnish with fresh parsley if desired.
If you need more info on butterflying chicken breast you can find plenty of tools/tips online. Basically slice the chicken breast horizontally without cutting all the way through, so that when you open it, it's a larger and flatter chicken breast.
Everyone's stove top cooks differently, especially depending on the skillet you use. If the heat ever seems too high like it is burning the chicken or sauce, reduce the heat to medium.
Great served with mashed potatoes, steamed veggies, or pasta!