I have lived in the U.S. as a green card holder (based on my employment as a professor) for three years. I have a unique opportunity to go teach and conduct research at an American university abroad on a six-year contract. Can I keep my green card?
It is possible to keep your green card when working abroad for an extended period of time, but it might be difficult.
If the American university where you intend to teach happens to be the American University in Beirut, or if you are pursuing this opportunity in the course of your duties as an employee of the U.S. government, then you are in luck — traveling with your green card (though it will have expired after one year of absence) should suffice to regain entry upon your return.
If neither scenario applies to you, however, you will need to file not one but four consecutive reentry permits (using Form I-131, available from U.S. Citizenship and Immigration Services or USCIS) — the first two being valid for two years each, and the last two being valid for only one year each.
Getting reentry permits would be especially needed in your case because the existence of your contract suggests that you would not qualify for a returning resident visa (as described on the "Returning Resident Visas" page of the State Department’s website) since such a visa would be available to you only if the length of your absence was due to circumstances beyond your control.
In addition, you would not seem to have a good enough excuse (or “good cause”) for simply showing up at the border and asking customs officers to let you reenter the U.S. as a returning resident in the exercise of their discretion. Instead, you would most likely be placed in removal proceedings, where you would get a chance to prove to an immigration judge that you have not really abandoned your permanent residence.
Still, the unusual length of your intended absence would likely raise suspicions in the eyes of both USCIS and customs officers. Suspecting that you have abandoned or intend to abandon your permanent resident status, USCIS officers could deny one or more of your reentry permit applications, and, even if they grant your applications, CBP officers could still deny you reentry.
To address these suspicions, you will need to be ready to present evidence that you have maintained ties to the U.S. — perhaps by not leaving with your entire family, or by maintaining a home or bank accounts in the States. It might also help to make sure that you already have a position to return to in the U.S. at the end of your contract, or that the contract provides for no more than six years of employment (for example, by stating explicitly that it cannot be renewed or extended).