Is there a chance to be a U.S. citizen if you're a granddaughter of a retired U.S. Army?

There's always a chance to be a U.S. citizen, but you don't leave enough information to say whether or not your grandfather's or grandmother's service in the U.S. military is going to be helpful on that front. I doubt it. You don't even mention your nationality, or your own personal qualifications. If you have a doctorate in medicine, you'll probably have a better chance than if your top skill is mowing lawns.