The Gemara in Shabbos 21b gives an explanation for Beis Shammai's opinion that one should count down candles throughout Chanukah that it's just like the karbanos of Sukkos which also counted down.
The latest time to bring Bikkurim is Chanukah, and the latest time, according to the Tanna Kamma, to say the accompanying passages is Sukkos (Bikkurim 1:6).
The Haftarah of the second day of Sukkos is that of the Chanukas HaBayis, paralleling the Chanukas HaMizbeiach of Chanukah. Remember, we say Mizmor Shir Chanukas HaBayis throughout Chanukah after Shacharis.
Chagai (Perek Beis) received a nevuah on Hoshanah Rabbah concerning Galus Yavan.
Both a Sukkah (Sukkah 2a) and a Menorah (Shabbos 22a) must be less than 20 amos tall.
And, of course, Maccabim 2:10:9-10 records that the eight days of Chanukah paralleled those of Sukkos, and they took Aravos and Lulavim to celebrate the neis that occurred.
Why are there so many parallels between Chanukah and Sukkos?