Gemara

36b (Mishnah): Any Mitzvah that is dependent on the land applies only in Eretz Yisrael.

37b: Tana d'Vei R. Yishmael says, had the Torah not taught that Bikurim apply only after conquering and dividing Eretz Yisrael, we would have learned from Chalah (which applied from the moment Yisrael entered).

Bechoros 27a (Shmuel): Terumas Chutz la'Aretz is Batel in a majority of Chulin.

Rabah would be Mevatel it (in a majority of Chulin), and eat it when he was Tamei.

(Shmuel): A Tamei Kohen may eat Terumas Chutz la'Aretz, unless the Tum'ah comes from his own body. Such Teme'im may not eat it, but they may touch it.

(Ravina): Therefore, a Nidah may separate Chalah for a young Kohen to eat. If no young Kohen is around, she takes it with a rod and burns it.

(Rav): A Tamei Mes may immerse and eat Terumas Chutz la'Aretz immediately.

The Halachah does not follow Rav.

Nidah 46b (Rabanan): Even according to the opinion that nowadays Terumah is mid'Rabanan, Chalah is mid'Oraisa. We find that during the 14 years of conquering and dividing, Yisrael had to take Chalah, but not Terumah!

Rejection (Rav Huna brei d'Rav Yehoshua): No. Rather, even according to the opinion that nowadays Terumah is mid'Oraisa, Chalah is mid'Rabanan;

(Beraisa) "B'Vo'achem" (plural) -- when all (i.e. the majority) enter. When Ezra brought the exiles back to Eretz Yisrael, the majority stayed in Bavel.

Beitzah 9a (Shmuel): One may eat bread of Chutz la'Aretz, and afterwards separate Chalah.

Rishonim

Rif (Pesachim 14b): Chalah of Eretz Yisrael is mid'Oraisa. It may not be eaten b'Tum'ah. Chalah of Chutz la'Aretz is mid'Rabanan. A young Kohen who has never seen Keri, or a Kohenes who has never been Nidah, may eat it. If no such Kohen is around, we burn it.

Rebuttal (Ba'al ha'Ma'or): An adult Kohen may eat it after immersing from Keri. No Tevilah is needed from Tum'as Mes! Rav Hai Gaon said so.

Defense (Hasagos ha'Ra'avad): Ravina, who is Basra, said that if no young Kohen is around, we burn Terumas Chutz la'Aretz. This shows that we conclude (unlike Rav) that Tevilah does not permit one who ever saw Keri.

Milchamos Hash-m (b'Sof): Even where there is no Kohen, we can Mevatel it to permit it to a Yisrael, like Rashi says! Some say that only when it became mixed with its own volume of Chulin, we may add Chulin to be Mevatel it.

Note: R. Aba (Beitzah 38a) taught that one's property cannot be Batel in another's. Perhaps even after b'Tum'ah, he must compensate the Kohen.

Rambam (Hilchos Terumos 1:26): Terumah is mid'Oraisa in Eretz Yisrael when most of Bnei Yisrael are there - "Ki Savo'u." Nowadays, it is only mid'Rabanan.

Rebuttal (Ra'avad): We hold like R. Yochanan, who says that nowadays Terumah is mid'Oraisa. The Rambam himself seemed to say so in Halachah 1. "Ki Savo'u" explains why Chalah is only mid'Rabanan nowadays.

Defense (of Rambam - Taz YD 331:1): Even the opinion that Terumah is mid'Oraisa nowadays, says that Chalah is only mid'Rabanan. The Rambam rules like the opinion that even Terumah, and surely Chalah, is mid'Rabanan!

Rebuttal (Nekudas ha'Kesef): All agree that Chalah is mid'Rabanan nowadays, due to "Ki Savo'u". No one applies "Ki Savo'u" to Terumah!

Rosh (Beitzah 1:13): (On Yom Tov,) Rashi forbids to eat and leave over only (he will later declare to be) Chalah, for this is like separating Chalah on Yom Tov. Rashi explains that Shmuel permits (on a weekday) to eat all the bread except for Kedei (a Shi'ur of) Chalah. If so, Shmuel should have said 'he leaves Kedei Chalah'! Rather, he said 'he eats, and later separates.' One must leave more than Kedei Chalah, for one must separate with a visible remainder. In any case, we learn that the Chalah need not be separated near the dough it exempts.

Rosh (Hilchos Chalah (after Menachos) 14): Rabah would be Mevatel Chalas Chutz la'Aretz in a majority, and eat it when he was Tamei. He was a Kohen. A Zar may not eat it. Some permit even to Zarim, and bring a proof from the Yerushalmi. The Ri says that the Bavli disagrees. Menachos 67a says that if a Nochri took Terumah in Chutz la'Aretz, it is not Medame'a (forbid a majority of Chulin, if it was mixed in). This implies that a Yisrael's Terumah in Chutz la'Aretz is Medame'a! The Ramban says that this is when it was mixed with an equal amount of Chulin. The Gemara did not say 'forbid', so we may infer that a Nochri's Terumah in Eretz Yisrael is Medame'a (forbids a majority of Chulin).

Poskim

Shulchan Aruch (YD 322:2): The Chiyuv Chalah mid'Oraisa is only in Eretz Yisrael, when all of Yisrael are there - "b'Vo'achem... ba'Achalchem mi'Lechem ha'Aretz. Chalah nowadays, and even in the days of Ezra, is only mid'Rabanan.

Shulchan Aruch (4): Nowadays, that every dough is Tamei due to Tum'as Mes, we separate one Chalah in Eretz Yisrael, one part in 48, and burn it.

Ramban (Chalah 22b before DH Rav Nachman): Some say that nowadays that there is no concern for confusion with Tahor Chalah, for there is no Taharah, even in Eretz Yisrael we separate only one Chalah.

Shulchan Aruch (5): Since there is no source mid'Oraisa for Chalas Chutz la'Aretz, a Tamei Kohen may eat it, unless the Tum'ah comes from his own body, e.g. a Nidah or Ba'al Keri it. One may separate one part in 48 and give it to a young Kohen who never saw Keri or Nidah, or an adult who immersed from Keri.

Rema: Some say that since Chalah is not eaten in Eretz Yisrael nowadays, everywhere we separate one Chalah and burn it. Our custom is to separate one Chalah of any size and burn it. The custom is to separate a k'Zayis.

Shach (9): The Maharshal says that nowadays we do not give Chalah even to minors, for we are not certain that they are Kohanim. The Maharil was concerned lest people say that Chalas Chutz la'Aretz may be eaten (even by adults). Mahariyo was concerned lest the child make crumbs and others will eat them. We give to young Kohanim only Chalah of Matzah on Pesach.

Shulchan Aruch (323:1): One may eat and afterwards separate Chalah of Chutz la'Aretz, since its whole source is mid'Rabanan.

Rema: One must leave a little more than the amount he will separate, so there will be a remnant to what he separates.

Shulchan Aruch (ibid.): One may not eat bread of Eretz Yisrael before separating Chalah.