In a mixing bowl, combine the shredded chicken, mayonnaise, celery, and onion. Mix until everything is evenly combined.
Season the chicken salad with salt and pepper to taste. Keep in mind that the mayonnaise may already be salty, so you might not need to add too much.
Toast your slices of bread if desired. Then, spoon the chicken salad mixture onto one slice of bread.
Top the chicken salad with your desired toppings, if using. Add another slice of bread on top to create a sandwich.
Cut your sandwich in half and enjoy! These sandwiches are perfect for packing in a lunchbox or serving as a quick snack.