In a bowl, combine yogurt, garlic, lemon juice, mustard, salt and pepper and whisk until smooth. Spoon about 1/2 cup into a gallon-sized zip-top bag. This will serve as your chicken marinade. To the rest, stir in parmesan cheese (this will be your dressing). Cover and refrigerate dressing until ready to use.
Slice chicken breast diagonally into long, 3/4-inch wide strips. Place cut chicken into plastic bag with marinade. Seal, then smush around until chicken is evenly coated. Refrigerate for at least 3 hours or overnight; take chicken out of refrigerator about 30 minutes before you plan to cook it.
Preheat a grill to high, or a grill pan or skillet set over medium-high heat. Lightly oil grill or skillet.
Remove chicken from bag, scraping off excess marinade. Cook, flipping only once, until both sides are browned and internal temperature (measured using a digital thermometer inserted in the thickest part of the piece) reads 165 degrees F. Cook time will vary depending on the cooking method used. When done, remove from heat and let cool slightly, then coarsely cut into bite-sized pieces.
Wash and dry romaine, then cut crosswise into 1/2-inch wide ribbons. Place in a bowl along with 1/2 cup of reserved yogurt dressing. Toss until evenly coated.
To warm pita, wrap in a single layer of damp paper towels and place on a microwave-safe plate. Stretch a layer of plastic wrap tightly over top. Microwave for 30 to 45 seconds or until pita is heated through. Carefully remove plastic wrap (it will release hot steam). Slice each pita in half and gently pry open the pocket.
Spread a spoonful of yogurt dressing on the bottom of each pita. Stuff with lettuce and tomatoes and top with grilled chicken. Enjoy immediately.