On daf יב עמוד א, the discussion is about bringing matnot kehuna on Yom Tov. In a מעשה שהיה, the gemara reads:

רב טובי בריה דרב נחמיה הוה ליה גרבא דחמרא דתרומה אתא לקמיה דרב יוסף אמר לו מהו לאמטויי לכהן האידנא א"ל הכי אמר רב יהודה אמר שמואל הלכה כרבי יוסי.

Our question is, this took place in Bavel (which is were Rav Yosef lived). So how did it come up that there was a sheila that someone would want to bring teruma to a kohen on yom tov? Even if it were wine from Eretz Yisrael, how could the kohen use it?

I heard recently (and didn't know before) that under some circumstances (I guess barring any additional tuma besides טומאת מת) that kohanim in chu"l could eat challah from chu"l. And of course, challah is taken in chu"l (I assume that today there are not kohanim who would actually eat it). So is it possible that a similar situation existed for terumah in Bavel? That terumah from Bavel produce would be taken and given to an appropriate kohen? The above incident happened in Bavel, not in a place that would be סמוך לארץ ישראל, right?

If you have the answer to this question or any ideas, we'd be happy to hear.

(Michael is my cousin and learns with his father once a week by phone)