The rabbinic work that records the debate between Beit Shammai and Beit Hillel on Hanukkah lights is the Talmud.
The discussion appears in the Babylonian Talmud, tractate Shabbat 21b. Beit Shammai taught that eight lights should be lit on the first night and one fewer each night afterward. Beit Hillel taught the practice now followed by most Jewish communities: begin with one light and add another on each successive night.
The Talmud explains Beit Hillel’s position with the principle that holiness should increase rather than decrease. Beit Shammai’s view was associated with the declining number of bulls offered during the eight days of Sukkot. The debate concerns the preferred way to fulfill the mitzvah, building on earlier descriptions of Hanukkah lighting.
The Talmud is not the same as the Mishnah, although it contains and discusses Mishnah passages. The Hanukkah lighting debate is a classic example of the Talmud preserving competing legal opinions while recording which approach became normative.