HEAT butter and olive oil in sauté pan over medium heat; be careful not to burn the butter, if using it. Add chicken breasts - do not crowd the pan. Sauté for about two minutes per side. REMOVE to a warm platter; you can place platter in warm oven.
ADD lemon and wine to pan; DEGLAZE (Dissolve the remaining bits of food) the pan using a wooden spoon or spatula to scrape. This is the basis for your sauce.
BRING to a simmer, reduce heat to medium-low, let sauce thicken.
WHEN sauce is thickened, swirl in butter. Add capers.