Hanukkah begins at sundown today, and U.S. Thanksgiving begins at midnight tonight.
It is a result of a rare coincidence between the lunisolar Hebrew calendar (whose dates reflect both the moon phase and the time of the solar year, and which can have between 353 and 385 days per year) and the Gregorian calendar. Because the calendars are not calculated the same way, Chanukah appears at a different time each year on the Gregorian calendar.
Thanksgiving Day has fallen during Hanukkah at least twice between 1863 (when Thanksgiving was proclaimed a U.S. federal holiday by President Abraham Lincoln) and 2013: in 1888 Thanksgiving was the first day of Hanukkah, and in 1899 it was the fourth day. Thanksgiving occurred later in those two years than is possible under current U.S. law (as a result of changes between 1939 and 1941); as a result of this confusion, some media reports have mistakenly claimed that Thanksgivukkah has never occurred since Lincoln.
Because the Gregorian and Jewish calendars have slightly different average year lengths, over time they drift out of sync with each other. As a result of this, Thanksgiving Day will not fall entirely within Hanukkah again in the foreseeable future. (One physicist has calculated that, if the Jewish calendar is not revised, Thursday, November 28 will not fall during Chanukah again until the year 79811.)  However, since the Jewish day does not begin at midnight, but on the sunset before it, those celebrating both holidays will light the second candle of Hanukkah 2013 the evening of Thanksgiving Day, the first candle having been lit on Wednesday, November 27; there will continue to be occasional years in which Hanukkah and Thanksgiving partially overlap, with the first night of Hanukkah beginning in the evening of Thanksgiving. For example, 2070 will be one such year, when the first night of Hanukkah will be the evening of Thursday, November 27. 1918 was another such year.