It's called the y chromosome. If she has one in EVERY CELL in her body its a boy. If you have one in NO CELL in your body, you're a girl. Case closed.
I respectfully disagree.
Women have two X chromosomes, men have one X and one Y. There is information on "extra" leg of the 2nd X chromosome that is "missing" on the Y chromosome, and that determines the sex of the child. I think we'd both agree thus far.
Now, what if that same information was "missing" from the extra leg of the 2nd X chromosome? We already know that the gender gene isn't the only information on that extra leg - it's how women can be carriers of some genetic diseases but not be afflicted themselves. So, it's entirely possible that the information could be missing from the second X chromosome as well.
What if you also have two X chromosomes to go with that Y? Then what are you? The story is so poorly written we can't tell what the heck the genetic situation is.