OISS sponsors employment based green cards (legal permanent resident status) for ladder track faculty and select senior researchers. However the decision to apply for citizenship (or naturalization, for those who were not born in the U.S.) is a personal one, and the university can not advise on the process or the application. Many people find the application forms fairly easy to complete, others prefer to have a qualified immigration attorney assist them. Please contact OISS if you would like the names of area immigration attorneys. If you’d prefer to begin the process by doing your own research, here are some resources:
You can also search the internet and read what different law firms say about the application process, for example here is a firm some in the Yale community have used before.