The Navi in (Melochim 2, 4) writes that the wife of one of the nevi'im, a widow, cried before Elisha that she has debtors, who want to take her children as slaves for the debt. Elisha told her (ibid. 4:3) הַחוּץ מִן כֵּלִים לָ ךְ שַׁא ֲלִי לְכִי תַּמְע ִיטִי אַל רֵק ִים כֵּלִים שְׁכ ֵ נָיִ ךְ כָּל מֵאֵת , "Go borrow vessels for yourself from the outside, from all your neighbors – empty vessels. Do not be sparing." She had a drop of oil in her home, and miraculously, the oil increased, and she poured it into all the utensils. On the words (ibid. 4:6) הַכֵּלִים כִּמ ְלֹאת וַיְהִי, "When all the containers were full," the Radak quotes from a Midrash that the woman said to her son, "Bring me the broken vessels." She said to her son, "HaKadosh Baruch Hu made a miracle that the oil filled all the utensils. HaKadosh Baruch Hu can make a miracle that the broken utensils will become fixed." Her son gathered the broken utensils. He piled them up, one on top of the other, and they all combined and became one large utensil, and the oil filled those utensils, as well.
Then the son said, כֶּלִי עוֹד אֵין, that there aren't any more utensils, and then הַשָּׁמֶן וַיַּע ֲמֹד, the oil stopped.
Let us learn from this episode that each person should prepare "utensils" to accept the light of Chanukah and the light of the Chanukah lecht. He should prepare himself for this mitzvah. One shouldn't say, "I am not able to prepare myself properly. All I can do is prepare some broken utensils." Broken utensils are sufficient to receive Hashem's wondrous light. Hashem will fix the utensil so that it can hold the light...
One way to make a hachanah and prepare oneself for Chanukah and for Chanukah lecht is to study Torah. Rebbe Menachem Mendel of Kotzk zt'l said that the chachamim concealed the light of each yom tov in the divrei Torah that discusses that yom tov. This is especially true for Chanukah. The Yevanim wanted תורתך להשכיחם, that the Yidden should forget Torah. It is therefore obvious that we won't be able to receive the lights of Chanukah without the light of Torah.
The Gemara (Shabbos 21b) elaborates on the halachos of Chanukah, and then it asks, מאי חנוכה , "What is Chanukah?" Shouldn’t it be written in the opposite order? First, the Gemara should describe חנוכה מאי, "What is Chanukah? Which miracle occurred for which we have this holiday?" After that, the Gemara can give the halachos. But we can answer that a person must first learn a daf Gemara, and then he can understand מאי חנוכה , what Chanukah is all about. But if he doesn't study Gemara, he won't be able to understand חנוכה מאי, what Chanukah is.
Another indication of the importance of studying Torah on Chanukah is the renowned question of the Beis Yosef (siman 670) on Chanukah, which has many, many answers.
I think there is no other question like this one that has so many answers. HaKadosh Baruch Hu arranged it that way to teach us that the yom tov of Chanukah is about learning Torah in depth, and making true chidushim.
