In a large stock pot, bring chicken stock, water, carrot, celery, onion, bay leaf, and peppercorns to a boil.
Reduce the heat to low and simmer for 15 minutes or until vegetables are tender.
Add chicken to the pot and simmer for 20 minutes or until chicken is cooked through.
Remove the chicken from the liquid and shred it. Discard any skin, bones, or fat.
In a bowl, mix together mayonnaise, lemon juice, celery seed, salt, and white pepper.
Add shredded chicken to the mixture and stir until combined.
Add celery and mix until ingredients are evenly combined.
Serve chilled or at room temperature with your favorite sides.