With an immersion blender in a wide mouth pint jar, blend all aioli ingredients.
Mix celery, onion, chicken, dill, and aioli in a medium sized mixing bowl.
Open a lettuce leaf on a plate and lightly crush the stiff main stem with the bottom of a cup. Do this by lightly pounding on the main stem of the leaf with your cup a couple of times. This will help the leaf roll without breaking.
Add 1/3 cup of the chicken salad to the middle of the leaf and rollup the end and sides, like a burrito. Salad can also be simply served on a bed of lettuce.