Originally written by Benjamin Maron for the InterfaithFamily blog, January 2013. Correction added at the end. 

I know, it's only January, so why am I talking about Hanukkah? And, worse, why are others also talking about it? Because while Hanukkah has come close to overlapping with Thanksgiving before (even in our lifetimes; we shared articles when it last nearly happened in 2002, Using Thanksgiving Leftovers the Next Day for Hanukkah and Not Your Typical Jewish Family), it will actually overlap this year! Hanukkah 2013 will be a unique calendar anomaly. Brace yourself for Thanksgivukkah!

Never before has Hanukkah started on [American] Thanksgiving. (I'd like to pause and mention that it has never and will never overlap with Canadian Thanksgiving, though Sukkot frequently does. And that at least makes sense: both are harvest festivals.) "Well, the last time it would have happened is 1861. However, Thanksgiving was only formally established by President Lincoln in 1863. So, it has never happened before." Cool, eh? [See update at the end - correction!] 

Why's that? It all has to do with the Hebrew calendar, which uses a 19-year cycle, and the fact that Thanksgiving, set as the fourth Thursday in November, will repeat its date every 7 years.

Jonathan Mizrahi explains:

The first day of Hanukkah coincides with Thanksgiving, on 11/28/2013. I was curious how often this happens. It turns out that it has never happened before...and it will never happen again.
Thanksgiving is set as the fourth Thursday in November, meaning the latest it can be is 11/28. 11/28 is also the earliest Hanukkah can be. The Jewish calendar repeats on a 19 year cycle, and Thanksgiving repeats on a 7 year cycle. You would therefore expect them to coincide roughly every 19x7 = 133 years. Looking back, this is approximately correct.... Why won't it ever happen again?
The reason is because the Jewish calendar is very slowly getting out of sync with the solar calendar, at a rate of 4 days per 1000 years (not bad for a many centuries old calendar!). This means that while presently Hanukkah can be as early as 11/28, over the years the calendar will drift forward, such that the earliest Hanukkah can be is 11/29. The last time Hanukkah falls on 11/28 is 2146 (which happens to be a Monday). Therefore, 2013 is the only time Hanukkah will ever overlap with Thanksgiving. You can see the start date of Hanukkah as a function of time in the attached plots. In the long timescale plot, the drift forward is clear.
Of course, if the Jewish calendar is never modified in any way, then it will slowly move forward through the Gregorian calendar, until it loops all the way back to where it is now. So, Hanukkah will again fall on Thursday, 11/ the year 79,811.

Further, my buddy Josh explains:

For there to have been any overlap at all in the past 100 years or so (i.e. since the definition of Thanksgiving became the current one), you need the earliest possible Hanukkah (first candle 11/27) and the latest possible Thanksgiving (11/28). The only time that is happening is this year. Having Hanukkah a day later relative to T-day (either Thanksgiving and the first candle both on 11/27, or both on 11/28), on the other hand, has/can/will happen a couple times. But this is the only time in our lives or our parents lives that ALL of Thanksgiving has been / will be on Hanukkah.

Again I say: cool, eh?

But wait, there's more! If you're really curious about how the Hebrew calendar works, how it drifts (when compared to our Gregorian calendar), how this affects other Jewish holidays in 2013, where President Roosevelt fits in (and he does), the difference between "applesauce years" and "sour cream years" and so much more, I encourage you to join Mah Rabu in geeking out over all of this on his blog. (Make sure to check out the comments (he'll answer them!) both on his blog and on Jewschool, where he's crossposted.)

Still not convinced? Mizrahi even made charts to demonstrate the calendar phenomenon. Impressive! (Visit his site for larger versions.)

Corrections: Jonathan Mizrahi has added an addendum to his original blog post, noting that this Thanksgivukkah phenomenon happened in 1888, when Thanksgiving was still on the last Thursday of the month instead of the 4th Thursday of the month. Head to his blog to read all the details.