Using fork, blend chicken, onion, celery, 1/4 cup stuffing, 2 tablespoons oil, 1 tablespoon lemon juice, tarragon, lemon peel, salt, and pepper in large bowl. Form mixture into eight 1/2-inch-thick patties. Sprinkle with 1/4 cup stuffing, pressing to adhere. Turn over and repeat. Working in 2 batches, heat 2 tablespoons oil in large skillet over medium-high heat. Add patties and cook until brown and cooked through, about 2 1/2 minutes per side. Transfer burgers to plate and tent with foil. Add 2 tablespoons oil and 3 tablespoons lemon juice to skillet. Bring to boil, scraping up browned bits. Season with salt and pepper and drizzle over burgers.