Zot Chanuka
Many parallels exist between the holidays of Chanuka and Sukkot. The basic parallel is that both are holidays of eight days, but the likeness runs much deeper.
According to one early source, the holiday itself was modeled on Sukkot. At Sukkot the soldiers were in the field and were unable to observe the holiday; when they conquered and purified the sanctuary they observed a new holiday, which was like a second Sukkot. (Maccabees II:10:6, mentioned in Arukh HaShulchan 670:5.)
Beit Shammai draw a significant halakhic parallel, explaining that the number of lights diminishes one each night, from eight to one, on the analogy of the bulls sacrificed at Sukkot, whose number diminishes from thirteen on the first day to seven on the last. (Shabbat 21b. Beit Hillel do not necessarily dispute the analogy to Sukkot, only the likeness of the lights to the bulls.)
The Mishna indicates that Bikurim (first fruits) can be brought until Chanuka; one understanding is that this is the very end of the olive harvest, which begins around Sukkot. (Bikkurim 1:6.) This suggests that Chanuka and Sukkot have a reciprocal relationship similar to that of Pesach and Shavuot, which correspond roughly to the beginning and end of the barley harvest. The Midrash states that the offerings of Kayin and Hevel were either at Chanuka or Shavuot, implying a similar relationship. (Bereshit Rabba on 4:3.)
The Sefat Emet writes that the likeness to Sukkot is the basis for another unique halakhic aspect of Chanuka: the existence of a distinct "mehadrin" (beautified) level of observance. We strive to beautify all mitzvot, but generally this augmentation is merely quantitative and doesn't involve a distinct way of fulfilling the mitzva. But on Chanuka, "hidur" means that we add one light each night. This reminds us of Sukkot, where the quality of "hadar" or beauty is not just an advantage in the commandment of the four species but is actually an inherent aspect of the mitzva. (Sefat Emet 5640, citing Rav Yaakov Meir of Gur. "Hadar" in four species: see Mishnah Berurah 645.)
According to this analogy, we can see the last day of Chanuka as a likeness of Shemini Atzeret, a distinct holiday that comes at the close of Sukkot. The last day of Chanuka is also considered in some ways a distinct holiday, which is known as "Zot Chanuka" after the Torah reading for this day.
According to Beit Shammai, the halakhic parallel is complete: On Shemini Atzeret we offer only a single bull; this can be likened to the single light lit on that night according to the approach of Beit Shammai. The seventy bulls offered during Sukkot correspond to the seventy nations, who are also bidden to celebrate this holiday (Zekharia 14:17). The single bull offered on Shemini Atzeret corresponds to Israel; on this day we commune alone with HaShem (Rashi Vayikra 23:36). The diminishment of the lights, like the diminishing number of bulls, corre- sponds to the waning power of alien ideologies that gradually leave the stage until only the pure light of Torah belief is left.
According to Beit Hillel we can draw the parallel similarly. The first seven days commemorate the waxing radiance of the light of Torah, the pirsumei nisa that spreads the light of our faith to the entire world. After seven days this process is complete, as a seven day cycle indicates perfection and comple- tion. The eighth day adds a special distinct level of enlightenment and sanctity that is unique to the people of Israel. Our religion strives to spread the light of holiness to the entire world, to create a true brotherhood of mankind. Ultimately we will be successful in this challenge. The eighth day of Chanuka reminds and reassures us that even when we succeed, the uniqueness of our people will never become superfluous. We will always maintain our special distinct holiness as the "nation of priests" (Shemot 19:6).