Shred 4 cups cooked chicken breast into bite-sized pieces and place in a large mixing bowl.
Dice celery until you have 1 cup; add to the bowl with the chicken.
Thinly slice green onions to make 1/2 cup; add to the bowl.
Drain large green olives if needed and slice them crosswise to make 1 cup; set the sliced olives aside.
In a separate bowl, whisk together 2/3 cup mayonnaise, 1 tablespoon green olive brine, 1 tablespoon fresh squeezed lemon juice, 1 teaspoon Dijon mustard, 1 teaspoon celery seed, and salt and fresh ground black pepper to taste until smooth.
Pour the dressing over the chicken, celery, and green onions; toss gently until evenly coated.
Carefully fold the sliced green olives into the dressed chicken mixture so they keep their shape. Taste and adjust salt and fresh ground black pepper as needed.
Serve immediately or cover and refrigerate. The salad will keep in the refrigerator for several days.