Remove the skin from the chicken and pull the meat from the bones. Discard the skin and bones.
Chop the chicken and put it into a medium bowl. Add the celery, scallions, walnuts, tarragon, and mayonnaise; mix thoroughly. If the mixture is not creamy enough, add more mayonnaise. Season with salt and pepper, to taste. Cover and refrigerate for 1 hour to let the flavors meld.
Slice the mini pitas in half, open the pockets, and stuff with a heaping tablespoon of chicken mixture.