This topic has been covered a couple of times before on the site, but I don't mind touching on it again, especially as I receive quite a few questions about it. The latest was just this week from a young man named Daniel. Here's a copy of his email:

Hi my name is Daniel. I am currently trying to get citizenship but I am not sure if I can get it because my grandfather was born in the US. I was just wondering if I would be allowed to get it if he had it at the time of my birth even though he wasn't born in Ireland. My mother didn't have citizenship at the time of my birth.

Well Daniel, it'd be inappropriate for me to do anything else other than to point you to the official info on this topic. The requirements are very likely to change over time and it'd be neglectful of me to post anything here other than what is current status, and a link to finding official information on the subject.

The table below is a snapshot of current (Sept 2017) eligibility requirements. It is a little complicated, but for those of you familiar with your family history, you can probably figure it out quiet easily.

 

If you are: Then you are:
A Born in the island of Ireland on or before 31 December 2004 Entitled to Irish citizenship or you are an Irish citizen
B Born on the island of Ireland on or after 1 January 2005 Entitled to Irish citizenship if one or both of your parents:

  • Is Irish
  • Is British or entitled to live in Northern Ireland or the Irish State without restriction on their residency
  • Is a foreign national legally resident in the island of Ireland for 3 out of 4 years immediately prior to your birth
  • Has been granted refugee status in Ireland
C Child of A, born outside the island of Ireland An Irish citizen
D Child of C and a grandchild of A, born outside the island of Ireland Entitled to Irish citizenship, but you must first register in the Foreign Births Register
E a child of D and a great-grandchild of A, born outside the island of Ireland Entitled to Irish citizenship, by having your birth registered in the Foreign Births Register, but only if your parent D had registered by the time of your birth.

Source:
http://www.citizensinformation.ie/en/moving_country/irish_citizenship/irish_citizenship_through_birth_or_descent.html#l97318

Important: For something as important as citizenship qualification, I want to re-clarify that this website is not the source of official information. You should check with the appropriate authorities for any immigration questions.