In a shallow container, combine the olive oil, lemon juice and zest, garlic, and salt and pepper. Add the chicken and turn to coat. If you have the time, marinate the chicken in the fridge for 2 to 6 hours before grilling – no worries if not.

Make the Caesar dressing: In a container with a lid, add the olive oil, mayonnaise, lemon juice, Dijon, Worcestershire sauce, garlic, anchovy (if using), salt and pepper. Cover tightly and shake to combine well. Add half the Parmesan and shake again to combine.

Preheat the grill to medium high. Grill the chicken for 5 to 6 minutes per side, until cooked through, with nice grill marks on each side. Let the chicken cool slightly, then cut into small bite-sized pieces.

In a large bowl combine the chicken, romaine, and red onion with the dressing. Add the remaining Parmesan and toss again. Fill each wrap with about 1½ cups of the salad (see above!), tuck in the ends, and roll closed.