Combine all ingredients in a bowl or freezer bag. Add chicken and toss well to combine.
Marinade for 30 minutes (or up to 4 hours) before cooking chicken.
Preheat grill to medium-high heat.
Place chicken on the grill for 7-8 minutes. Flip over and cook an additional 7-8 minutes or until no pink remains and chicken reaches 165°F. Rest 3-5 minutes before slicing.
Balsamic Glaze:
Add balsamic vinegar to a small pot. Bring it to a boil, then reduce the heat and simmer for 10-15 minutes or until the sauce reduces to a syrup and coats the back of a spoon.
Assemble wrap with lettuce, tomato, fresh mozzarella, basil leaves, sliced chicken and drizzled balsamic glaze. Fold wrap and cut in half on a diagonal.