In a large resealable plastic bag, combine the olive oil, lemon juice, garlic, oregano, salt and pepper.
Add the chicken and turn to coat. Seal the bag and refrigerate for at least 1 hour.
Preheat the grill to medium-high heat.
Remove the chicken from the marinade and discard the marinade.
Grill the chicken for about 5 minutes per side or until cooked through.
Let cool slightly before slicing into thin strips.
To assemble the wraps: Place a tortilla on a flat surface. Top with lettuce, chicken strips and Parmesan cheese. Roll up tightly and cut in half. Serve immediately.