The following explanation was developed by Rabbi Zolly Claman, now of Edmonton, Canada.
With a better understanding of Sukkos, perhaps we can get a better understanding of its connection to Chanukah. The eight days of Sukkos consist of the seven days of the festival of Sukkos and conclude with the festival of Shemini Atzeres. During the first seven days, there are a total of seventy bulls that are brought as offerings. These seventy bulls represent all the nations of the world1, commonly categorized into seventy nations2. The eighth day, Shemini Atzeres, requires only one bull offering. This lone bull represents the nation of Israel.
The idea of these offerings is that after all is said and done, the Jewish people are Hashem’s unique nation. After all the nations in the world partake of the party of Sukkos, Hashem specifically asks us to stick around for one extra day3. Sukkos culminates in a single offering, showing the intimate relationship G-d has with the Jews4 5. We are described as Hashem’s unique portion6, and the eight-day festival of Sukkos makes that clear.
Until the Greek subjugation, all nations of the world knew the Jewish people’s uniqueness. Indeed, this was often the cause for antisemitism. The Greeks were the first to have the audacity to question this unique relationship with Hashem. They were bold enough7 to claim that we had no portion in Hashem8. They felt that the Torah was just another intellectual pursuit, and was just as much theirs to learn. It belonged with their study of math and science and philosophy. There was nothing unique to the Jewish people. The Greek’s many decrees against Judaism were to emphasize this belief.
When the Maccabees defeated the Greek army, there was no better way to celebrate than to celebrate similar to the festival of Sukkos. The Greek’s denied the uniqueness of the Jewish people, and Sukkos epitomizes that uniqueness. Although Chanukah became its own distinct holiday, it still shares aspects with Sukkos. This is because it reestablished the Jewish people’s unique role in history, and confirmed their intimate relationship with Hashem.
1 Sukkah 55b
2 For example, see Midrash Tanchuma Noach § 3, Bamidbar Rabbah 2:3, Rashi to Exodus 2:14
3 Sukkah loc. cit.; Rashi to Leviticus 23:36 and Numbers 29:36
4 See Ma’aseh Rav § 233 for a deeper insight into this differentiation
5 See Meshech Chochmah parshas VeZos HaBeracha (end) who uses this to explain why we read parshas Vezos HaBeracha on Shemini Atezeres, and it’s not because that’s when we finish the Torah. Even those that completed the Torah every three years would read every Shemini Atezres Vezos HaBeracha. It’s also why we read I Kings Chapter 8 for the haftarah (Megillah 29b).
6 Maharsha to Sukkah loc. cit. s.v. הני ע' פרים
7 The Greek empire is symbolized by a leopard (Daniel 7:6, see Rashi ad. loc.), which is associated with boldness (Avos 5:20)
8 Bereishis Rabbah 2:4. This is to directly combat the idea expressed by the Maharsha loc. cit.