I'm sure I saw info about going about this on one of the embassy's websites -- either the Embassy of Ukraine in Kiev or its website in the U.S. Google both and go see. If you can prove you were born in Ukraine, getting your Ukrainian citizenship will be easy and pretty straightforward. But be warned, if you take on Ukrainian citizenship they are one of the few backward countries in the world which do not tolerate dual citizenship. They insist on a written correspondence between you and the country where you are currently a citizen that proves you have renounced that country's citizenship! So do your research.