To make the soup, bring the chicken stock, water, celery, carrots, onion, bay leaves, and peppercorns to a boil in a medium saucepan.
Add the chicken breasts, making sure they are completely covered with liquid by at least an inch. Stir the chicken occasionally until it is cooked, then reduce the heat and simmer for 20 to 30 minutes.
Cool chicken breasts by removing them from the oven. Alternatively, you can save the broth and use it again to make chicken salad!
After the chicken is cooled, shred it into 1-inch pieces and stir it with the mayonnaise, lemon juice, celery seed, salt, and pepper until well combined.
Refrigerate for 24 hours in an airtight container.
As soon as you are ready to serve, give the salad a good stir, and taste, and adjust the seasoning as necessary, adding salt as necessary. Hope you enjoy it!