Cover chicken with water in a large stockpot. Bring to a boil and cook chicken until tender and fully cooked. While warm, remove meat from bones and discard skin, cool and finely dice. Combine chicken with juice, salt, celery and mayonnaise. Mix well. Refrigerate for at least 2 hours, preferably overnight.
Cut crust off of the bread slices. Cut bread slices in half diagonally. Sandwich with the chicken salad.