In a blender or food processor, blend the avocado, lemon juice, olive oil, basil, salt, and pepper until smooth and creamy, scraping sides as needed. Set aside.
In a medium bowl, combine chicken, celery, red onion, grapes, apples, and nuts.
Stir in avocado dressing with other ingredients. Add additional salt and pepper to taste.
Enjoy on bread, on top of leafy greens or in a lettuce wrap!