Boil chicken breasts in a pot filled with water until no longer pink in the centers and juices run clear, about 40 minutes.

While chicken finishes boiling, preheat an outdoor charcoal grill for medium-high heat and lightly oil the grate. Place approximately 10 coals off to one side and light; coals are ready when they have some white dust.

Add hickory chips to a container or on aluminum foil on top of coals. Place chicken breasts onto the preheated grill as far away from the heat as possible.

Smoke chicken just until a light smoke is apparent, no more than 15 minutes. Transfer chicken to a plate to cool, about 10 minutes.

Dice each chicken breast; sprinkle with pepper and celery salt. Place diced celery and red onion in a large bowl; add chicken 3 breasts at a time, sprinkling with 1 pinch caraway seeds and mixing well after each addition. Stir in mayonnaise. Cover and refrigerate until ready to serve.