- Combine teriyaki sauce, green onions and ginger; pour over chicken in large plastic food storage bag. Press air out of bag; close top securely. Turn bag over several times to coat all pieces well. Refrigerate 45 minutes, turning bag over once.
- Remove chicken from marinade; discard marinade.
- Cook chicken on grill 4 to 5 inches from hot coals about 6 minutes on each side, or until chicken is no longer pink in center.
- To serve, spread both halves of rolls with mayonnaise; place chicken on bottom halves and cover with top halves.