Grill the chicken breasts until fully cooked, then dice them into small pieces.
In a mixing bowl, combine the diced chicken, mayonnaise, chopped celery, Dijon mustard, salt, and black pepper. Mix well.
Toast the bread slices.
Assemble the sandwich by spreading the chicken salad mixture on a slice of toasted bread. Top with shredded lettuce and tomato slices, then cover with another slice of toasted bread.