During the eight days of Hanukka we read the Tora in the morning. Now, what Biblical text was chosen by the Rabbis to be read on Hanukka and why?
Let me first explain the question. On every Jewish Holiday we read in the Tora a portion corresponding to the story of that specific Holiday. During the eight days of Pesah, for example, we read eight Tora portions alluding to the Exodus from Egypt, the Mitsvot of Pesah, the Pesah sacrifice, etc. But the events of Hanukka happened around the year 160 BCE and were not recorded in the Tanakh (Hebrew Bible). The Rabbis, therefore, had to find a Biblical text to be read that somehow would be related to Hanukka.
Our Rabbis chose the section of Naso in the book of Numbers ("In the desert" chapter 7), dealing with the inaugural offerings of the tribal leaders at the time of the dedication of the mizbeah (=the altar of the Tabernacle).
1. Hanukka means "inauguration" or "dedication". In Hanukka we celebrate that once the Greeks were defeated the Jews re-dedicated the altar of the Temple--which was defiled by pagan offerings-- to HaShem. The Parasha we read is about the dedication of the mizbeah of the Tabernacle, our first Temple. This seems to be the original reason for reading Perashat Naso. But there is more to this story.
2. In the dessert, the Tabernacle was completed on the 25 of Kislev. Coincidently, this is the same day we celebrate Hanukka.
3. On the last day of Hanukka, we read the paragraph dealing with the lighting of the Menora, which remind us of the miracle of the oil in the times of Hanukka.
4. The book Me'am Lo'ez brings an additional reason. If you pay close attention to the offerings related in Perashat Naso, you will see that the tribe of Levi did not participate of the dedication of the altar. During Hanukka the Hashmonayim--Cohanim descendants of the tribe of Levi-- were the ones who recovered and rededicated the altar.