"I Have had a green card for nearly seven years, and for family reasons I will be moving back to Ireland in the next several weeks. The possibility of my returning here in the future is slim, but still, I would like to become a U.S. citizen. Is it possible to do this at the American Embassy in Dublin? I have paid taxes every year, have never been in trouble with the law and have been a productive resident for my whole time here. Will it be possible to become a citizen abroad?"
No it will not. If you are going to be a full-time resident of Ireland in the next few weeks, you will not be able to complete the naturalization process, which is a shame because you seem to be qualified in every other way.
The law as regards to naturalization says that the citizenship candidate must have resided in the U.S. for the five-year period immediately preceding the filing of the application (three years if married to a U.S. citizen). Also, the applicant must have continually resided in the U.S. from the date of application until the time that naturalization is granted.
The latter requirement clearly won't apply in your situation, as you'll be living in Ireland. The vast majority of naturalization interviews take place at U.S. Citizenship and Immigration Service offices in the U.S. (A notable exception is made for members of the armed forces.)
If you choose, you have the option of keeping your permanent resident status alive by filing for a re-entry permit (Form 1-131) prior to departure from the U.S. The permit allows the holder to remain outside the U.S. for up to two years and re-enter the country with resident status intact.
The filing fee is $305. The form and further instructions are available at www.uscis.gov.
Speaking of our armed forces, members who are not U.S. citizens are given special consideration with regards to naturalization, should they wish to go through the process.
Those on active duty, or recently discharged, can avail of a streamlined, relatively fast process for naturalization. They are also not required to pay the processing fee of $675.
Many of the requirements necessary for naturalization must be met by armed forces members, including knowledge of English, U.S. government and civics. But members do not have to prove residency and U.S. physical presence requirements - in other words, they do not have to accumulate five years of permanent resident status to start the process, nor do they need to have spent at least half of that time in the U.S.
Another benefit all immigrants who have served honorably on active duty in the U.S. Armed Forces or as a member of the Selected Ready Reserve on or after September 11, 2001 are eligible to file for immediate citizenship. This section also covers veterans of designated past wars and conflicts.