On each of the eight days of Chanukah we read from the section in Parashat Naso that describes the "Chanukat Ha'nesi'im," the offerings brought by the tribal leaders for the inauguration of the Mishkan. If the reader mistakenly read from the weekly Parasha, rather than reading the special selection for Chanukah, the congregation has nevertheless fulfilled their obligation, and they are not required to now read the Chanukah reading (Chacham Ovadia Yosef, Chazon Ovadia Laws of Chanukah, p. 239, based on Masechet Megila 29).
When Rosh Chodesh Tevet (which always occurs during Chanukah) falls on a weekday, we read three Aliyot from the standard Rosh Chodesh reading, followed by one Aliya from the Chanukah selection. This arrangement is in accordance with the famous Talmudic principle of "Tadir Ve'she'eino Tadir, Tadir Kodem," which requires affording precedence to the more frequent Mitzva. Since Rosh Chodesh occurs more frequently than Chanukah, we conduct the Rosh Chodesh reading before the Chanukah reading.
If a congregation removed two Torah scrolls from the ark for the reading on Rosh Chodesh Tevet, but the reader mistakenly read four Aliyot from the Rosh Chodesh reading, they must open the second scroll and read a fifth Aliya for Chanukah. Otherwise, they would be infringing upon the honor of the second Torah scroll, Heaven forbid, by removing it from the ark without reading from it. If on Rosh Chodesh Tevet the reader began reading from the Chanukah selection, rather than first conducting the reading for Rosh Chodesh, he should complete the Chanukah reading in a single Aliya, and then read three Aliyot from the section for Rosh Chodesh. (Based on Chazon Ovadia Laws of Chanukah, p. 240)
