Lengthwise cut chicken into 3/4-inch-wide strips. Set aside.
Place flour on wax paper. In shallow dish, stir together egg whites and water. In another shallow dish, combine Cheez-It® cracker crumbs, Parmesan cheese and oregano.
Roll chicken pieces, one at a time, in flour. Shake off excess flour. Dip into egg white mixture then coat with the cracker mixture, gently pressing breading onto chicken. Place in a single layer in a shallow baking pan coated with cooking spray or lined with foil.
Bake, uncovered, at 425°F for 15-20 minutes or until chicken is no longer pink. For food safety, internal temperature of the chicken should reach at least 165ºF.