Cut bell pepper in half lengthwise; discard seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 15 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel and finely chop.
Prepare grill to medium-high heat. Combine bell pepper, cheese, olives, and basil. Cut a horizontal slit through thickest portion of each chicken breast half to form a pocket. Stuff 2 tablespoons bell pepper mixture into each pocket; close opening with a wooden pick. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon black pepper.
Place chicken on a grill rack coated with cooking spray. Grill 6 minutes on each side or until done. Remove from grill; cover loosely with foil, and let stand 10 minutes.