Well, you have to have a parent or a grandparent born in Ireland, then you have to prove it. The Irish Consulate has a packet and forms and all kinds of stuff. I had to get my grandmother's birth certificate, marriage certificate, death certificate, then my father's birth and marriage certificate and all my ID, also have to provide photos, a sign off from a lawyer, and everything has to be notarized and all that muck. Throw in $180 bucks and wait 10 months or so and you get entered into the register of foreign births. Once that is complete, you can file for an Irish passport, and then you are good.
I made sure to talk with the US State department before I did it (I was hired by them, but on a list to be deployed, till the war started and my security clearance ran out), its not a problem to have a dual citizen ship, it is a good thing to have if you want to work, or own property or business in the EU.
Make sure I am right, but I have researched this fairly thoroughly. If no one ever has a reason to search this fact out, and you never have any enemies, I suppose you could risk it, but I know I would not consider losing my American citizenship for anything.