Heat the olive oil in a large skillet over medium-high heat. Season the chicken breasts with salt and pepper. Place chicken in the skillet, and cook until browned on each side, about 5 minutes per side.
Reduce heat to medium, and add the butter and garlic. Saute for about 3 minutes. Pour in the gin, vermouth, lemon juice, and olives; simmer for 5 to 10 minutes, until the sauce thickens and chicken juices run clear.