It is possible to derive citizenship from your parents who could have derived it from your grandparents. It is a complicated analysis to determine whether or not citizenship was derived. It would be beneficial for you to contact an immigration attorney.
Great-grandparent? Perhaps, but it's a long shot that will need some very complex analysis.
The information offered is general in nature and not meant to be relied upon as legal advice. Please consult an attorney prior to making legal decisions. Visit us at www.tunitskylaw.com. Contact us at 713.335.5505 or email at firstname.lastname@example.org. Veronica Tunitsky offers in-person, as well as telephone and email consultations.