Am I eligible for U.S. citizenship?

Your facts are too sketchy to determine whether your father was ever a US citizen which would be crucial to any determination of whether the right to citizenship was transmitted to you. Even if he was, he would have had to have resided in the US for five years of which two were over the age of 14 prior to your birth in order to transmit citizenship.Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.  

You must analyze whether your parents derived citizenship from your grandmother and then if they did so, you must analyze whether you obtained citizenship from your citizen parents.  Here is a link that will help. http://www.uscis.gov/policymanual/PDF/NationalityChart3.pdf