Simmer chicken in a pot of water over medium heat to an internal temperature of 160°F. Remove from water. Dice chicken into small bitesized pieces and refrigerate to cool fully.
Once cooled, thoroughly mix the chicken, onion, celery, dill, and mayo, in a bowl. Season with salt and pepper to taste.
Spoon the chicken salad onto the lettuce, top with onion and tomato. Serve with chips and pickles.