1. Preheat oven to 375°.
2. Tear off 4 (12-inch) lengths of heavy-duty aluminum foil; fold each piece of foil in half, shiny sides together. Place on a baking sheet, and open out flat, shiny side up. Coat with cooking spray.
3. Arrange one-fourth of chicken strips on half of each aluminum foil square near the crease. Spoon vegetables evenly over chicken; sprinkle with basil and 1/2 teaspoon pepper. Drizzle 1 teaspoon olive oil over vegetables in each packet. Fold aluminum foil over chicken and vegetables, bringing edges together; fold edges over to seal securely. Pleat and crimp edges to make an airtight seal. Bake at 375° for 30 minutes.
4. Remove chicken mixture from packets, and transfer to individual serving plates. Or, if desired, place packets on individual serving plates; cut an opening in the top of each packet, and fold aluminum foil back. Sprinkle each serving with 1 tablespoon Parmesan cheese. Serve immediately.
Note: If desired, fill foil packets with chicken and vegetables the night before and chill. Bake at 375° for 35 minutes.