Gemara

(Mishnah): If a (childless) man went overseas with a wife and left a wife (Leah) home and they told Leah that he died, she may not remarry nor do Yibum until she hears whether or not she, her Tzarah, is pregnant.

119b - Question: Can she never remarry?

Answer #1 (Ze'iri): She must wait three months for herself (lest she is pregnant), and nine months for her Tzarah. After this Leah does Chalitzah, and she is permitted l'Shuk whether or not her Tzarah bore a child.

Answer #2 (R. Chanina): She must wait three months to see if she herself is pregnant. She must wait forever for her Tzarah!

Question: Why can't Leah do Chalitzah after nine months, whether or not her Tzarah had a child?

Answer (Abaye bar Avin and R. Chanina bar Avin): This is a decree, lest the Tzarah had a child, and we will have to announce that the Chalitzah was unnecessary and void, so Leah is permitted to a Kohen.

Question: What is wrong if we need to announce this?!

Answer: Perhaps someone who saw the Chalitzah will not hear the announcement. When he sees her marry a Kohen, he will think that a Chalutzah was permitted to a Kohen.

(Mishnah): If a woman says 'I had a son overseas. He died, and then my husband', she is believed. If she says 'My husband died, and then my son', she is not believed. We are concerned for her words; she does Chalitzah, not Yibum.

Question: We should be concerned lest witnesses come and verify her story, and we will have to announce that she is permitted to a Kohen!

Answer #1 (Rav Papa): That Mishnah discusses a divorcee.

Answer #2 (R. Chiya brei d'Rav Huna): The case is, she said that she and her husband were alone in a cave. We are not concerned lest witnesses come.

36a - Question (R. Elazar): Our Mishnah refutes R. Yochanan (who says that Chalitzah is valid even if one of the widows is pregnant!

Question: Granted, she cannot do Yibum, lest her Tzarah have a viable baby, and Leah is Eshes Ach (with no Mitzvah of Yibum), an Isur mid'Oraisa. But why can't she do Chalitzah?

Granted, she cannot do Chalitzah and marry within nine months due to this concern (lest the Tzarah is pregnant). But why can't she do Chalitzah within nine months and marry after nine months? (This shows that Chalitzah is invalid if a widow is pregnant!)

Counter-question: Also according to Reish Lakish, why can't she do Chalitzah after nine months, and then marry!

Answer #1 (Abaye bar Aba): We are concerned lest the Tzarah give birth to a viable baby;

Even if we would make a proclamation that Leah is permitted to a Kohen, perhaps someone who saw the Chalitzah will not hear the proclamation.

Answer #2 (Abaye): The Mishnah does not say she may not do Chalitzah or Yibum. It says that she may not remarry nor do Yibum, i.e., without Chalitzah. If she does Chalitzah, she is permitted!

41a (Mishnah): A Yevamah may not do Yibum or Chalitzah within three months of the death of her husband.

41b - Question: Granted, she may not do Yibum within three months, lest she is pregnant. Why is Chalitzah forbidden?

Suggestion: Our Mishnah refutes R. Yochanan, who says that Chalitzah of a pregnant woman is valid.

Answer: No. We forbid Chalitzah lest she give birth, and we will need a proclamation that she is permitted to a Kohen (and someone will not hear...)

Rishonim

Rif and Rosh (16:1): The Halachah follows R. Chanina, for in Perek 4 we establish the Mishnah like he does.

Rebuttal (Ba'al ha'Ma'or): No! There, Abaye concluded that the Mishnah does not forbid her to do Chalitzah, it only forbids her to remarry without Chalitzah! It seems that we rely on R. Zeira, since he is supported by (Abaye and) the text of the Mishnah. It does not say that she may not do Chalitzah!

Defense #1 (Milchamos Hash-m): The first answer there was the Stam Gemara (it explained the problem of needing a proclamation), which is more authoritative than an Amora. All the more so we follow it against Abaye, for Abaye said only that the Mishnah does not refute R. Yochanan. He could establish it to discuss a divorcee (for whom no proclamation is needed), so it does not oppose R. Chanina! We find that Ze'iri was R. Chanina's Talmid; the Halachah follows the Rebbi. Abaye bar Avin and R. Chanina bar Avin hold like R. Chanina. They are the majority (against Abaye). Rav Papa and R. Chiya brei d'Rav Huna are Basra, and they explain R. Chanina.

Defense #2 (Nimukei Yosef DH Gemara, citing the Rashba): Also R. Yochanan holds like R. Chanina.

Rambam (Hilchos Yibum 3:16): If Leah's husband and his other wife (Rachel) went overseas and they told Leah that he died, she may never do Chalitzah or Yibum until she hears whether or not Rachel gave birth. Why can't she do Chalitzah nine months after he died? If Rachel bore a viable child, there is no need for Yibum or Chalitzah. If Rachel did not bear a viable child, Leah's Chalitzah was valid! This is a decree lest later we hear that Rachel bore a viable child, and one who did not hear this will see her marry a Kohen and testify that Beis Din permitted a Chalutzah to a Kohen. Therefore, if she was already forbidden to a Kohen she may do Chalitzah after nine months.

Lechem Mishneh: Rashi explains that Leah must wait three months (from when her husband left) lest she herself is pregnant, and nine months for Rachel (lest Rachel is pregnant). The Rambam explains that Rachel must wait three months lest she herself is pregnant (e.g. they left at least six months ago, so after three more months we are not concerned lest Leah is still pregnant) and Leah must wait nine months.

Poskim

Shulchan Aruch (EH 156:13): If Leah's husband and his other wife (Rachel) went overseas and two told Leah that he died, she may not do Chalitzah or Yibum until she knows whether or not Rachel gave birth. If Leah was already forbidden to a Kohen she may do Chalitzah after nine months.

Rashbash (in R. Yerucham 25:1:216, cited in Beis Yosef DH Kasuv): I am unsure whether or not it helps for Leah to vow Al Da'as Rabim (subject to the volition of at least three people) that she will never marry a Kohen. We rely on vows to eliminate concerns regarding money, Isurim and bodily punishment. E.g. if one divorces his wife, she may not collect from an Arev (guarantor) or from what he made Hekdesh lest this is a scheme, unless he vows not to remarry her. A Kohen who married a woman b'Isur may serve after forbidding her through a vow. A rapist is lashed for uprooting the Mitzvah to marry his victim through a Neder Al Da'as Rabim.

Ginas Veradim (EH 2:5, cited by R. Akiva Eiger): It is proper that he did not resolve his doubt! In many places Chachamim strengthened their enactments to include cases where the reason does not apply. A woman must wait three months before remarrying to avoid doubt about who is the father, even if she was Arusah, sterile, Ailonis or too old to give birth. This was a fence lest people transgress the decree itself. If one married a woman pregnant with or nursing another man's baby, the Poskim obligate him to divorce her. It is not enough to vow not to benefit from her until she will be permitted (after 24 months of nursing). We cannot learn from collecting from Hekdesh or an Arev, for those are not enactments mid'Rabanan. However, we find that Chachamim allow a divorcee to do Chalitzah after nine months. This suggests that Chalitzah is forbidden only when there is concern lest she later marry a Kohen. It seems that one may be lenient. Chachamim gave leniencies even about mid'Oraisa laws (e.g. to rely on one witness of death) to prevent Igun (inability to remarry). If we are not lenient here, she will be an Agunah her entire life! Also, we are concerned lest she act immorally if we do not permit her.

Beis Meir (DH v'Im): If her husband went alone and there were rumors that he married there before he died, the Rivash (509) permits Leah to do Chalitzah before the rumors are verified, but not to do Yibum.