Place chicken in a large baking dish. Spread pink salt and 1 tablespoon pepper evenly inside the cavity. Stuff the cavity with celery.
Coat chicken skin with olive oil. Sprinkle with remaining pepper and kosher salt.
Roast in the preheated oven until the juices run clear and an instant-read thermometer inserted into the thickest part of the thigh, near the bone, reads 165 degrees F (74 degrees C), about 1 1/2 hours.
Cover chicken with aluminum foil and allow to rest for 10 minutes before serving.