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Mix oil, 1 teaspoon each of the garlic powder and Italian seasoning, and 1/4 teaspoon of the pepper in small bowl. Place chicken in large resealable plastic bag or glass dish. Add marinade; turn to coat. Refrigerate 15 minutes or longer for extra flavor.
Meanwhile, mix mayonnaise, sour cream, Parmesan cheese, milk, remaining 1/2 teaspoon each garlic powder and Italian seasoning, and 1/4 teaspoon pepper in small bowl. Cover. Refrigerate until ready to serve. Remove chicken from marinade. Discard any remaining marinade.
Grill over medium heat or broil 6 to 7 minutes per side or until chicken is cooked through. Cut chicken into strips. Spread dressing evenly on tortillas. Top with lettuce and sliced chicken. Fold tortilla over and serve.