What is the earliest day in the year that Chanukkah has ever fallen on?

In 1994, Hanukkah fell unusually early on the calendar (November 28 to December 5). I'm not all that certain it's a record.

https://www.hebcal.com/holidays/chanukah-1994

Jersey City customarily displays the menorah on the Plaza lawn to the left of the main entrance to City Hall and the crèche on the lawn to the right. Because the Hanukkah festival normally overlaps with the Christmas season, the menorah and crèche are usually displayed at the same time. In 1994, however, when the present action was initiated, Hanukkah fell unusually early on the calendar (November 28 to December 5). Consequently, the City took down the menorah display the day before it erected the crèche. The City also decorated an evergreen tree with Christmas ornaments on the Plaza lawn on December 14. Other than this tree, the crèche and menorah displays were unaccompanied by any other traditional secular symbols of the holiday season.

Because of the way the Jewish and Gregorian dates work out, the first night of Hannuckah can theoretically be anywhere from the 20th of November to the 18th of December. Though the extremes occur less commonly, once in a whil (once every 19 years), December 4th on the Gregorian is on the same day as the 3rd of Tevet in the Jewish calendar - the day AFTER the last day of Hannuckah, meaning the first day of Hannuckah in those years is the 25th of November (and the first candle is lit on the 24th in the evening. The next time this shall occur will be in the Jewish year 5774 - Gregorian 2013, when the first candle will be lit on November 25th.

The latest date that can serve as the first night of Hannuckah is December 26th, which happens once a lifetime or so (for astronomical reasons for which there isn't space to explain here). The next time this will occur will be in the Jewish year 5842 - Gregorian 2081.