Prepare outdoor grill with hot coals, or heat gas grill to hot, or heat oven broiler.
Combine ground chicken, cream cheese, bread crumbs, grated onion, salt, pepper, rosemary, cheddar cheese and parsley in large bowl. With greased hands, form mixture into 6 equal patties.
Grill or broil burgers for 4 minutes per side or until instant-read thermometer inserted in centers registers 165°F. Place on rolls; top with lettuce and tomato.