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.
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 ground 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 degrees for 30 minutes.
Remove chicken mixture from packets, and transfer to individual serving plates. Or, if you like, 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.