Place chicken in a single layer in a wide skillet that has a lid. Cover with water. Place skillet over medium heat and bring the water to a simmer. When the water has reached a simmer, cover and simmer until chicken is cooked through, about 10 minutes for tenders and 25 minutes for breasts. Remove from heat and transfer the chicken to a plate. Allow to cool, then cut into 1 inch cubes.
While chicken is cooling, prepare the dressing by adding the mayonnaise, lemon juice, and cayenne pepper to a medium mixing bowl.
Stir the chicken cubes, celery, green onions, walnuts and blackberries into the dressing. Taste the salad. If desired stir in sea salt and black pepper to taste. Place in an airtight container and refrigerate until ready to serve.