In a large bowl, using a potato masher or large whisk, coarsely smash most of the chickpeas (some of the chickpeas might still be whole, which is good).
Add the celery, onion, mayonnaise, and lemon juice to the chickpeas and mix well. Season generously with salt and pepper. Stir in the chives and parsley.
Spoon the chickpea salad into the lettuce leaves and serve.