Preheat oven to 350 degrees F. Combine onions, cheese, and bacon in a small bowl. Cut a 1-inch-wide slit into the thick end of each chicken breast, and carefully cut down to center of chicken to form a pocket. Divide cheese mixture evenly among pockets. Secure with wooden picks. Sprinkle chicken with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Heat a large ovenproof skillet over medium-high heat. Add the oil. Add chicken to pan; saute 4 minutes. Turn chicken over and place skillet in oven and bake for 12 minutes; let stand 5 minutes before serving.