Preheat oven to 400 degrees. In large skillet, sauté bacon over moderate heat until crisp. Drain, break into pieces, and place in food processor. Puree the bacon, basil and garlic to a paste. With machine on, add olive oil in a thin stream. Transfer to a small bowl, add lemon juice, and just enough grated cheese to form a thick paste.
Make a horizontal incision in each piece of chicken to form a pocket. Spoon 1 TBS of stuffing into each pocket, and press to close, using wooden toothpicks, if desired.
Lightly flour the chicken, dip in egg, and coat with breadcrumbs. In a large skillet, over moderately high heat, melt butter and add oil. Add chicken and brown on all sides. Place chicken in baking dish, and finish in oven (approximately 12-15 minutes, check with thermometer). 4 servings.