Following a discussion about what is permitted to be used as kindling for Shabbat candles the Talmud turns is attention to what can be used for the Chanukiya:

Rav Huna said: Those wicks and oils with which the Sages said that one may not light the lamp on Shabbat, one may not light the lamp with them on Hanukkah either; both when it falls on Shabbat and when it falls during the week. Rava said: What is the reason for Rav Huna’s statement? He holds that if the Hanukkah light becomes extinguished, even though one lit it properly, one is bound to attend to it and relight it so that it will burn properly. Therefore, one must ensure that the wick burns properly from the outset. And utilizing the light of the Hanukkah lamp is permitted during the week. Consequently, in order to prevent him from inadvertently sinning on Shabbat, he must ensure from the outset that the wick burns well, lest he come to adjust the flame on Shabbat. Those wicks and oils do not burn well at all. And Rav Ḥisda said: Those same oils and wicks with which the Sages prohibited to light on Shabbat, one may light with them on Hanukkah during the week, but not on Shabbat. He holds that if the Hanukkah light is extinguished

... The Sages taught in a baraita: The basic mitzva of Hanukkah is each day to have a light kindled by a person, the head of the household, for himself and his household. And the mehadrin, i.e., those who are meticulous in the performance of mitzvot, kindle a light for each and every one in the household. And the mehadrin min hamehadrin, who are even more meticulous, adjust the number of lights daily. Beit Shammai and Beit Hillel disagree as to the nature of that adjustment. Beit Shammai say: On the first day one kindles eight lights and, from there on, gradually decreases the number of lights until, on the last day of Hanukkah, he kindles one light. And Beit Hillel say: On the first day one kindles one light, and from there on, gradually increases the number of lights until, on the last day, he kindles eight lights. ... What is Hanukkah, and why are lights kindled on Hanukkah? The Gemara answers: The Sages taught in Megillat Ta’anit: On the twenty-fifth of Kislev, the days of Hanukkah are eight. One may not eulogize on them and one may not fast on them. What is the reason? When the Greeks entered the Sanctuary they defiled all the oils that were in the Sanctuary by touching them. And when the Hasmonean monarchy overcame them and emerged victorious over them, they searched and found only one cruse of oil that was placed with the seal of the High Priest, undisturbed by the Greeks. And there was sufficient oil there to light the candelabrum for only one day. A miracle occurred and they lit the candelabrum from it eight days. The next year the Sages instituted those days and made them holidays with recitation of hallel and special thanksgiving in prayer and blessings. We learned there in a mishna with regard to damages: In the case of a spark that emerges from under a hammer, and went out of the artisan’s workshop, and caused damage, the one who struck the hammer is liable. Similarly, in the case of a camel that is laden with flax and it passed through the public domain, and its flax entered into a store, and caught fire from the storekeeper’s lamp, and set fire to the building, the camel owner is liable. Since his flax entered into another’s domain, which he had no permission to enter, all the damages were caused due to his negligence. However, if the storekeeper placed his lamp outside the store and it set fire to the flax, the storekeeper is liable, as he placed the lamp outside his domain where he had no right to place it. Rabbi Yehuda says: If the flax was set on fire by the storekeeper’s Hanukkah lamp that he placed outside the entrance to his store, he is not liable, as in that case, it is permitted for the storekeeper to place his lamp outside. Ravina said in the name of Rabba: That is to say that it is a mitzva to place the Hanukkah lamp within ten handbreadths of the ground. As if it should enter your mind to say that he may place it above ten handbreadths, why is the storekeeper exempt? Let the camel owner say to the storekeeper: You should have placed the lamp above the height of a camel and its rider, and then no damage would have been caused. By failing to do so, the storekeeper caused the damage, and the camel owner should not be liable. The Gemara rejects this: And perhaps one is also permitted to place the Hanukkah lamp above ten handbreadths, and the reason Rabbi Yehuda exempted the storekeeper was due to concern for the observance of the mitzva of kindling Hanukkah lights. He held that if you burden one excessively, he will come to refrain from performing the mitzva of kindling Hanukkah lights. Since the storekeeper placed the Hanukkah lamp outside at the behest of the Sages, the storekeeper should not be required to take extra precautions. With regard to the essence of the matter Rav Kahana said that Rav Natan bar Manyumi taught in the name of Rabbi Tanḥum:

Since they were also part of the same miracle. Rashbam explained, that the primary part of the miracle was done by them; Purim - by Esther, Chanukah - by Judith, Pesach - for they were saved in the merit of the righteous ones of that generation. And this [interpretation] is difficult, for the language "since they were also" implies that they were secondary, and according to his [Rashbam's] interpretation, it should have said "since they were". Therefore, it seems to me, that they were also potentially going to be wiped out and killed, and so too on Pesach, when they were enslaved to Pharaoh in Egypt, and in Chanukah, the decrees applied to them too. In the matter of Matzah, there is one who asks why do we need this comparison, that everyone who is included in the prohibition of eating leavened bread is included in the positive commandment of eating Matzah. [Why not] learn it from them having been part of the same miracle? And it should be said, that this reason [part of the same miracle] does not obligate one but Rabbinically, so we need the comparison. And our Rabbi Joseph, of Jerusalem, explained that you might exempt them from it, by means of a comparison, for [Pesach] is on the 15th, and so too Sukkot is on the 15th [and women are exempt from the Sukkah], as I have explained in the chapter of Eilu Ovrin (Tosafot on Pesachim 43b:1).