The following is adapted from the Days of Joy, an anthology of ideas and insights of the Sfas Emes (Rabbi Yehudah Aryeh Alter of Ger) on Chanukah and Purim (Artscroll Judaica Classics 1995).
In a variant reading of the Gemara (Shabbos 22a), we find a source for the custom of the master of the house wearing a tallis while kindling the menorah:
“[מזוזה מימין ונר חנוכה משמאל [ובעל הבית בטלית מצויצת באמצע”
In order to appreciate the significance of this custom, we might recall the following encounter between Noah’s children.
Hearing that their inebriated father was lying exposed to the public, Shem (the ancestor of the Jewish people), and Yefes (from whom the Greeks descended) jointly covered Noah (Breishis 9:23). For this kindness, they were amply rewarded with regal vestments. Specifically, Shem’s descendants were graced with the mitzvah of tzitzis. Yefes and his children, among them the Greeks, were blessed with lavish clothing and the surface veneer of sophistication in the form of Hellenistic culture.
On Chanukah, we commemorate the victory of the Jewish tallis-wearers over the Greek spear-bearers.
It is true that halachically, one who kindles the menorah is not obligated to wear a tallis. Nonetheless, we don the tallis as a proclamation against the fiendish intentions of the Greeks to assimilate us. We will never betray G-d’s commandments! After all, is it not the primary purpose of tzitzis “so that you may remember and perform all My commandments” (Bamidbar 15:40) ?