Using a sharp knife, make a straight vertical cut down the center of the chicken breast half, but do not slice all the way through. Holding your knife at an angle, start to open up one side of the breast half so it will be able to lay flat. Gently pull the widening flap open as you cut, making short scraping cuts to free the flap of meat at the narrow end. Turn the breast half around and repeat to open up the other side. Spread both sides of the breast open and make short shallow cuts, then pound to equal thickness with the flat side of a meat mallet or small heavy pan. Repeat with other chicken breast half.
Season chicken paillards on both sides with salt and pepper. Heat olive oil and butter in a large skillet over medium-high heat until butter foams. Add paillards and saute on one side until golden brown, about 2 minutes. Reduce heat to medium. Flip and saute paillards until cooked through, about 2 minutes. Transfer to serving plates.