Although religiously observant Jews are careful to wear their nicest clothes on certain holidays, they are not particular about what they wear on Hanukkah. The eight-day holiday features a ritual lighting of a menorah, or eight-branched candelabra, to recall the miracle of oil found in the temple. The oil was only enough for one day, but it burned for eight.
A Rabbinic Holiday
The holiday of Hanukkah does not appear in the Bible, so its status is different than that of major holidays, including Rosh Hashana and Passover. Hanukkah is a rabbinic holiday, meaning the rabbis proclaimed it a holiday after the Bible was completed. The obligations and restrictions that apply on biblical holidays, such as refraining from certain types of work, eating special meals and wearing festive clothing, don't apply to Hanukkah.
Shabbat Hanukkah
Because Hanukkah lasts more than a week, one day of the holiday inevitably falls on Shabbat, the Jewish Sabbath. The Talmud asserts that one way a person honors Shabbat is by wearing nice clothing. These clothes should be clean and nicer than what one wears during the week. On Shabbat Hanukkah -- the Shabbat that falls during the holiday -- individuals who regularly observe Jewish law wear the clothing they normally wear on Shabbat.