Shred the cooked chicken breasts into small pieces into a large bowl.
In a food processor, add the grapes, celery and green onions and pulse until they are about the size of a pea, but not pureed! Add the minced grapes and veggies to the chicken.
Stir in the mayonnaise and salt and pepper. Mix until well combined. Taste and adjust the seasoning by adding more salt and/or pepper if needed.
Refrigerate for 1 hour or up to 3 days before serving.