Kristi has been asking me some interesting questions about celebrating Chanukah as a Christian. I can address this a bit more specifically as a Catholic.
Let me start by saying I am not a historian, theologian or scientist. My statements are based solely on my personal beliefs within the framework of the Bible and the Catholic church.
For several years now, I have hoped to commemorate Chanukah in our home. I would like to emphasize to my children that Chanukah is not the "Jewish Christmas" as many erroneously believe it to be, that instead it celebrates the triumph of Judah the Maccabee and his brothers for their victory over foreign armies and the return of the Temple to the Jewish people. The miracle culminated when there was not enough oil found to light the lamp in the Temple but the lamp burned for seven days and eight nights.
Why would a Christian, or more directly, a Catholic want to celebrate Chanukah? For me that is answered by Paul in several of his epistles. Paul identifies Christians as spiritual descendents of the Jews. Paul was unique in his time in that he converted not only Jews, but Gentiles as well. Before Paul, many saw Christianity as a branch of Judaism. As a spiritual descendent, I feel it is important to honor my spiritual heritage by celebrating many of the traditions that come along with it. Technically, I celebrate Passover every week as that was the meal Jesus was presiding over during the Last Supper.
The problem we run into as Christians when we decide to celebrate the traditions of Judaism, is doing so respectfully. When I was in high school, Adam Sandler first played the Chanukah Song on Saturday Night Live. While it certainly gave Chanukah a fresh face, it also played on stereotypes and played up the non-religious aspect of gift giving ("eight crazy nights"). It is one thing to have the symbols, it is quite another to say the prayers and teach the significance of the dreidel and it's characters. My advice is to seek out any friends you may have who happen to be Jewish or contact a local temple or synagogue and ask for guidance. We are blessed in our town to have 3 temples, at one of which is a rabbi who seeks to find unity amongst religions. In fact, after becoming close personal friends with our previous priest over (of all things) a viewing of The Passion of the Christ at behest of the local paper, this rabbi has done a Passover sedar meal each year as a fund raiser on Palm Sunday.
As for the question as to whether Jesus would have celebrated Chanukah, again not being a scholar of history, theology or science, I believe he was a faithful and practicing Jew and would have participated in all of the traditions and religious ceremonies associated with Judaism. Yes, he would have celebrated Chanukah.