If the Jews are the chosen nation of G-d, then how could He allow the holocaust to happen to them?
We cannot know why G-d would allow the Holocaust to occur. However, we do know that the Torah predicts events such as the Holocaust if the Jewish People remain in exile. The Torah tells us that if the Jewish People choose to sin while living in Israel, it will start a long series of events that will begin with suffering in the land, followed by exile, followed by severe persecution. These events will ultimately lead the Jewish People to realize that their intense suffering could only be explained as G-d goading us to understand that we cannot survive without His favor. That realization will lead to our redemption. (All of this is clearly explained in Deuteronomy, especially the portion of Haazinu (Deuteronomy Chapter 32).)
In other words, being G-d’s chosen people does not just mean that we are privileged; it means we have the responsibility to shoulder His mission for the world. That is an immense privilege, but it also has tremendous risks.
May we enter the time of redemption soon.