Place the chicken breasts in a pot of water. Bring to a boil, then reduce heat to medium. Cook until chicken is no longer pink, and reaches an internal temperature of 170 degrees F. This will take about 18-20 minutes.
Place the cooked chicken breasts on a plate to cool. Slice each one in half to speed up the cooling process.
Put the cooled, cooked chicken breasts in the food processor, along with the onion. Pulse a few times until the chicken is finely chopped. Don't overdo it, you don't want a chicken paste.
Add the mayonnaise, salt, pepper, and dill. Stir.
Toast the gluten free bread.
Spread the chicken salad on 4 pieces of bread, and top with the other slices. You can add tomato slices and lettuce if desired.
Notes
If you aren't on an egg free diet, use your regular mayonnaise.You can use any type of bread that suits your dietary needs.If you can't eat onion, you can leave it out. Feel free to use celery or some fresh herbs instead.This chicken salad will keep in the refrigerator for three days.