Oil grill and preheat barbecue. Grate 1 cup (250 mL) zucchini. Using your hands, squeeze out as much liquid as possible. Whisk egg with lemon peel, salt and pepper. Add zucchini, chicken, bread crumbs and green onion. Work with a wooden spoon or your hands until well mixed.
Form into 4 burgers, each about 1 inch (2.5 cm) thick. Place on grill and barbecue until well done, about 6 to 8 minutes per side. Serve in warm rolls, nan or focaccia, topped with a dab of garlicky tzatziki dip or mayonnaise.