Gemara

(Mishnah - R. Meir): If one bought wine from Kusim (and cannot separate the tithes before drinking), he may declare "the two Lugim that I will later separate should be Terumah; 10 Lugim (that I will separate) are Ma'aser Rishon; nine are Ma'aser Sheni." He may drink immediately;

R. Yehudah, R. Yosi and R. Shimon forbid.

Gitin 25b: This shows that R. Yehudah and (R. Yosi and) R. Shimon hold that Ein Breirah.

Rejection (Rava): They could hold that Yesh Breirah. Here they do not allow relying on Breirah, lest the barrel break before he separates the tithes, and retroactively, he drank Tevel.

R. Meir is not concerned lest the barrel break.

Beitzah 9a (Rabah): If one kneaded a dough before Yom Tov, he may separate the Chalah on Yom Tov.

Shmuel's father: Even if he kneaded a dough before Yom Tov, he may not separate the Chalah on Yom Tov.

Suggestion: Shmuel argues with his father, for Shmuel taught that in Chutz la'Aretz one may eat bread and afterwards separate Chalah. (Since he could eat before Hafrashah, it should be permitted to separate!)

Rejection (Rava): Shmuel agrees that once one called it Chalah it is forbidden to Zarim (therefore it may not be separated on Yom Tov, just like Terumah and Ma'aser).

36b (Mishnah): We do not separate Terumah or Ma'aser on Yom Tov, and all the more so on Shabbos.

37a. If they became Tevel today, e.g. a dough was kneaded on Yom Tov, we may separate Chalah and give it to a Kohen.

Rishonim

Rif: The Halachah follows Shmuel's father, like it says on 37a. If it became Tevel today, e.g. if a dough was kneaded today, we may separate Chalah and give it to a Kohen.

Rebuttal (Rosh Beitzah 1:13): Rabah permits because one may eat Terumah of Chutz la'Aretz before Hafrashah, therefore it does not look like Tikun. Shmuel's father disagrees because it becomes forbidden to Zarim. Rabah agrees about Terumah of Eretz Yisrael, since one may not eat it before Hafrashah. If so, we cannot learn from 37a, for it explains the Mishnah, which discusses Eretz Yisrael!

Defense #1 (Milchamos Hash-m): Rabah and Shmuel did not mention Chutz la'Aretz. This implies that they argue even about Chalah of Eretz Yisrael. R. Yehudah permits Ha'alas Meduma (when Chulin fell into Terumah, we separate from the mixture and consider it to be Terumah and permit the rest) because one may eat it without physical separation. (It suffices to mentally decide where the Terumah will be.) Nevertheless, Chachamim forbid. It appears that even R. Yehudah permits only regarding Meduma, for it was originally Terumah and he calls it Terumah. He agrees that one may not separate Chalah, for it was originally Chulin. Surely, Rabah permits even in Eretz Yisrael, but only regarding Chalah. Because the majority was kneaded today, even what was kneaded yesterday is permitted. For the sake of Simchas Yom Tov, Chachamim did not distinguish.

Rambam (Hilchos Yom Tov 3:8): If one kneaded a dough before Yom Tov, he may not separate the Chalah on Yom Tov.

Beis Yosef (DH Kasav Hagahos): Hagahos Maimoniyos says that one may eat and leave over only if the entire dough was kneaded together.

Beis Yosef (DH v'Chasvu Od, citing Hagahos Maimoniyos): Semak says that if one forgot to separate Chalah from Matzos, he must leaves over from each one. He joins them in a Kli after Yom Tov, and separates from one on all of them and on what was eaten. I say that it is proper to separate from each one. Joining in a Kli does not help for what was eaten.

Tosfos (Beitzah 9a DH Gilgel): If one forgot to separate Chalah from bread before Yom Tov, he eats and leaves over from each loaf. After Yom Tov he separates. He must leave over much, so the Shirayim (remainder) will be Nikarim (recognizable). If one forgot to separate from many loaves kneaded together, he leaves over one and separates from it on all of them. If one did not separate from Matzos, which are kneaded individually, he must leave over from each one, and after Yom Tov he puts all of them in a Kli and separates from each one. An easier solution is to knead and bake a new Matzah afterwards and join it to the remnants and separate from one on all of them, since the Chiyuv (for the new Matzah) came now.

Rosh (ibid.): R. Chaim says in the name of Rashi that eating and leaving over the Chalah is like separating on Yom Tov. It is forbidden. A case occurred, and Rashi forbade. Rashi explains that Shmuel permits eating everything except for the Shi'ur needed for Chalah. This is difficult. If so, Shmuel should have specified! Rather, he must leave over more than the Shi'ur, so later he can separate Chalah in a way that the Shirayim are Nikarim.]

Tur (OC 506): Since Rabanan argue about whether one may not separate Chalah on Yom Tov from a dough kneaded before Yom Tov, it is good not to separate. Rather, one eats and leaves over.

Beis Yosef (DH v'Kivan): Rabbeinu Chiya in the name of Rashi forbids this. The Tur is not concerned for his opinion, for it is an excessive stringency. Alternatively, the Tur's counsel is even according to Rashi. Rashi forbids leaving over only the amount needed for Chalah or a little more. This is truly like separating. The Tur permits if he leaves over much more than the Shi'ur. This is not like separating, for after Yom Tov he separates Chalah from much bread. When the Tur mentions Rashi's law, he says 'he leaves over the Chalah.' Regarding his own counsel, the Tur says 'he leaves over', without mentioning 'Chalah'.

Mordechai (Beitzah 654): If one kneaded a dough before Yom Tov, one may not separate Chalah on Yom Tov. One may not bake it on Yom Tov, for one may not eat it on Yom Tov. If one baked it before Yom Tov, one may eat it on Yom Tov, as long as he leaves over enough for Chalah, like Shmuel taught regarding Terumas Chutz la'Aretz.

Question (Beis Yosef OC 506 DH Kasav ha'Mordechai): When he only kneaded it before Yom Tov, why can't he bake it on Yom Tov? He can eat and leave over! The Poskim permit this.

Tosfos (ibid.): Do not say that we forbid covering the blood (of a bird or Chayah slaughtered on Yom Tov) but permit separating Chalah on Yom Tov, due to Simchas Yom Tov. Here we discuss Chutz la'Aretz, so one may eat and separate afterwards. It seems that no one disagrees.

Mahariyo (48): For mid'Rabanan laws we rely on Breirah (to say that it is as if he separated from the beginning - Beitzah 37b). Also, for Chalah of Chutz la'Aretz, we hold like Shmuel, who says that one may eat and separate later. This shows that Yesh Breirah.

Poskim

Shulchan Aruch (OC 506:3): One may not separate Chalah from a dough kneaded before Yom Tov.

Kaf ha'Chayim (28): Even if he separated b'Mezid, it is permitted. Normally, Chachamim forbid the food even if a mid'Rabanan transgression was done b'Mezid. Here we are lenient because the food was permitted without this. Also, we may rely on the Rishonim who rule like Rabah, who permits Hafrashah l'Chatchilah.

Rema: He may eat and leave over, and after Yom Tov he separates Chalah from what remains.

Gra (DH Ela): When a mental Hafrashah is required, one opinion in the Yerushalmi (Orlah 9a) forbids eating before doing so. Here, no such Hafrashah is required, so all permit.

Rema (ibid.): (If it was not baked before Yom Tov,) one may bake it on Yom Tov, eat some and separate Chalah after Yom Tov.

Mishnah Berurah (21): This refers to Chalah of Chutz la'Aretz. In Eretz Yisrael one may not eat before Hafrashah. The only solution is to knead more (and separate on both together), like the Rema says later.

Taz (7): Presumably, the Mordechai forbids baking it because the Chalah cannot be eaten on Yom Tov, just like one may not bake a dough owned jointly with a Nochri. Since he could have separated Chalah before Yom Tov, it is like something that can be divided. The Poskim say that one eats and leaves over, but he may not separate Chalah; they do not discuss baking. Perhaps this is b'Di'eved, when it was baked. This is slightly Dochek, but since Poskim do not explicitly oppose the Mordechai, we should be concerned for his opinion.

Mishnah Berurah (22): He must leave over a bit more than the Shi'ur, so when he separates afterwards the Shirayim will be Nikarim. Also, if he leaves over only the Chalah, this is like Hafrashah.

Shulchan Aruch (YD 331:70): In Chutz la'Aretz one may eat Tevel and separate afterwards.

Shulchan Aruch (323:1): In Chutz la'Aretz one may eat and afterwards separate Chalah, for the source of Chalah in Chutz la'Aretz is mid'Rabanan.

Birkei Yosef (2): A Sefer learns from Terumah that if one forgot to separate Ma'aser (before Shabbos), he may eat on Shabbos and separate after Shabbos. However, we permit this for Chalah of Chutz la'Aretz only because its source is only mid'Rabanan. This does not apply to Terumah and Ma'aser in Eretz Yisrael, for its source is mid'Oraisa! The Sefer wanted to say that the Beis Yosef wrote Bedek ha'Bayis after the Shulchan Aruch, and he retracted to say that it does not depend on having no source in Torah. This is wrong. Bedek ha'Bayis merely fixed the text of the Rambam like it says in Shulchan Aruch; the Shulchan Aruch was written afterwards.

Birkei Yosef (3): If one forgot to separate Chalah of Eretz Yisrael before Shabbos, one may not mentally separate on Shabbos to permit eating the bread.