The tractate containing the Talmudic discussion of Shabbat and Hanukkah lights is Shabbat. The key passage is Babylonian Talmud Shabbat 21b, where the rabbis discuss the kindling of Hanukkah lamps and how the practice commemorates the miracle of the oil.
The discussion asks practical questions, including where Hanukkah lights should be placed and how they should publicize the miracle. It also presents the famous account that, after the Temple was rededicated, one cruse of ritually pure oil lasted for eight days.
A common mix-up is Sukkah: Sukkah 46a discusses related details, including blessings over the Hanukkah lamp, but the classic Talmudic passage about the origin and rules of Hanukkah lighting is in Shabbat. The tractate’s name refers to the Sabbath, whose restrictions also affect Hanukkah lighting when the festival coincides with Friday night or Saturday.