Heat 1 tablespoon of olive oil in a nonstick skillet over medium heat. Season chicken breasts with salt and pepper, and cook for 5-7 minutes on each side until fully cooked. Let rest for 5 minutes before slicing.

Slice the cooked chicken into strips and toss with teriyaki sauce in a medium bowl.

Shred the carrots and red cabbage, and chop the romaine lettuce. Warm tortillas in a dry skillet for about 20 seconds on each side.

Spread mayonnaise on each tortilla if using. Layer sliced chicken, carrots, cabbage, and lettuce. Fold sides and roll tightly.

Slice each wrap in half and serve with additional teriyaki sauce.