In a large bowl, toss the chicken, scallions and celery to combine. Gently stir in the chopped avocado and 1 tablespoon of the lemon juice.
In a blender, combine the remaining avocado and lemon juice. Add the olive oil, vinegar, mayonnaise, parsley and dill. Puree until smooth. The mixture should be thick and about the consistency of mayonnaise. (If needed, thin the mixture with 1 to 2 tablespoons water.)
Pour the dressing over the chicken mixture and gently toss to coat. Season with salt and pepper. Taste and adjust flavors to suit you.
Store in an airtight container in the refrigerator until ready to serve. The salad will keep, refrigerated, for up 1 day.
Garnish with fresh dill.
You can also use the meat from 1 rotisserie chicken. Serve on a big leaf of Bibb Lettuce, or with crackers.