79,043

The only other time that the first day of Chanukah fell on Thanksgiving was in 1888, on November 29. At that time, Thanksgiving was celebrated on the last Thursday of the month.

Assuming no calendar or date changes, the next time this will happen will be in 79,043 years from now. At the moment, The earliest Chanukah can be is November 28, and the latest Thanksgiving can be is also November 28. But in a few years the Jewish calendar will shift a day wrt the general calendar, and the earliest Chanukah can fall will be November 29. This will shift gradually throughout the next 80 centuries until the calendars line up the way they are again.

But that is assuming no calendar changes. The Jewish calendar will have to be adjusted because Pesach must come in the spring. We can't have it shifting through the year.