Polygamy was permitted by the Torah, though it was later banned in most communities. Even though polygamy was still allowed, a man was not permitted to marry his wife’s sister, as this would be a source of bad blood. This particular prohibition remained in effect even if the couple divorced (because having your sister marry your ex would still be pretty aggravating) but if the wife died, the man could then marry her sister. (This mitzvah also prohibits extramarital relations with a wife’s sister, not just marriage.)
This law applies to a wife’s full sister or to a half-sister on either side, born in or out of wedlock or from a forbidden relationship. Rabbinically, if a man has an obligation of yibum (levirate marriage) with his late brother’s widow, her sister becomes forbidden to him even if he performs the chalitzah ceremony dissolving the bond. This is true even though he did not betroth her himself, but became “bound” to her through the death of his brother. (We’ll discuss yibum in Mitzvah #598 and chalitzah in Mitzvah #599, both in parshas Ki Seitzei.)
The general reasoning underlying all the arayos – a preventive measure regarding people of the opposite sex with whom we are overly familiar – applies here as well. Additionally, there is the aspect of not vexing the woman who is already married to the man by bringing her sister into the relationship. Such a relationship has the potential for disaster written all over it.
The obvious question is how Yaakov, the patriarch Jacob, could marry two sisters, Rachel and Leah. We have a tradition that the Avos (forefathers) kept the Torah before it was given, but marrying sisters is a clear violation of this injunction! There are many potential answers to this conundrum; I’ll share just one of them here.
If the Avos kept the Torah, they did so voluntarily, as it had not yet been commanded. When Yaakov proposed to Rachel, he made a commitment to marry her. Lavan (Laban) made a last-minute switch for Rachel’s sister Leah. This placed Yaakov in a bit of a bind. Normally, he would observe the Torah law not to marry sisters. However, he had given Rachel his word. Yaakov’s desire to voluntarily keep mitzvos could not override his obligation to keep his commitment to Rachel. (As you can see from the Biblical narrative, sharing a husband was indeed a source of unneeded stress to both sisters.)
This mitzvah applies in all times and places. It is a topic in the Talmud in the tractates of Yevamos (see, for example, 41a, 51b, 97a, et al.). It is codified in the Shulchan Aruch in Even Ha’Ezer 15. This prohibition is #345 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #131 of the 194 negative mitzvos that can be fulfilled today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.