It doesn't make scientific sense. 23 chromosomes from the mother bond with 23 chromosomes from the father to make 23 chromosome pairs. If something has 24 chromosomes, it has 12 chromosome pairs. Each chromosome matches with a compatible chromosome on the other strand. One of the 23 chromosome pairs determines sex.
When a person has one extra chromosome, that is, 22 pairs plus triplet, that person is classified to have one of a number of disorders, many of which are life threatening.
At least that is what I remember from school accompanied by some light internet reading. Basically the story doesn't make sense scientifically.