Heat oven to 400°F. Spray large cookie sheet with cooking spray.
In large resealable food-storage plastic bag, mix pesto and mayonnaise. In another large resealable food-storage plastic bag, mix bread crumbs and cheese. Place chicken in pesto bag; seal and coat with pesto mixture. Place chicken in bread crumb bag; seal and shake to coat. Place chicken on cookie sheet.
Bake 15 to 20 minutes, turning once, until chicken is no longer pink in center and bread crumbs are golden brown.