Based on my understanding this would be an eligible case. Let me know what you think!
Here is the situation:
Great-great grandfather (Achille Bongiorno) born in Messina, Sicilia. Immigrated to the US in 1902.
Great grandfather born in the US in 1910.
Achille naturalized in 1913.
Grandmother born in US in 1942.
Father born in US in 1968.
----
GGGF>GGF>GM>F
