Three Sifrei Torah
32. This year [5786], Rosh Chodesh Teves falls on Shabbos Chanukah. We take out three sifrei Torah and read the parshas hashavua, the parshah of Rosh Chodesh, and the parshah of Chanukah, in that order (שו"ע סי' תרפ"ד ס"ג ). The parshah of Rosh Chodesh precedes that of Chanukah based on the rule תדיר ושאינו תדיר, תדיר קודם (מ"ב סק"י ).
33. The parshas hashavua is divided into six or more aliyos (מ"ב סק"ט ). A Kohein should not get Acharon of the first sefer Torah since leining will not be completed from it (מ"ב סי' קל"ה סקל"ו ). After finishing the parshas hashavua, the second sefer Torah [for Rosh Chodesh] is placed next to it – Kaddish is not yet said – and hagbahah and gelilah are done on the first sefer. The second sefer is then opened and the parshah is leined in one aliyah. If there were seven aliyos from the first sefer, a Kohein may get Acharon from the second sefer.
Maftir
34. Kaddish. After leining the parshas hashavua and the parshah of Rosh Chodesh, Kaddish is said with the third sefer Torah [for Maftir of Chanukah] next to the second one (מ"ב שם סק"ט ). The Kaddish covers the first sefer Torah even if it is not on the bimah when the Kaddish is said (פמ"ג א"א סק"ה, מ"ב סי' קמ"ז סקכ"ז ).
35. If Kaddish was mistakenly said after the parshas hashavua was leined from the first sefer Torah, it is not repeated after leining the parshah of Rosh Chodesh (מ"ב סי' רפ"ב סקל"ד ).
36. Haftorah. The Chanukah haftorah [“רני ושמחי ”], not the Rosh Chodesh haftarah, is leined since פרסומי ניסא takes precedence over תדיר. Also, the last parshah leined is that of Chanukah and the haftorah should connect to the end of the leining (מ"ב סקי"א ).
Mistakenly Put Out Chanukah Sefer Before Rosh Chodesh Sefer
37. If, after leining the parshas hashavua, the Chanukah sefer Torah was mistakenly put on the bimah and the oleh already said “Borchu” and “Boruch atah Hashem” of the brachah, he should finish the brachah and they should lein the parshah of Chanukah. Afterward, they should lein the parshah of Rosh Chodesh and the haftorah of Chanukah for פרסומי ניסא even though they finished with the Rosh Chodesh leining. If they mistakenly leined the Rosh Chodesh haftorah, they are yotzei (ביא”"ל סי' תרפ"ד ד"ה ואם טעה ).
38. If they realized the mistake before the oleh said Hashem’s name in the brachah, even if he already said “Borchu,” they should close the sefer Torah, bring out the Rosh Chodesh sefer, and the oleh should make the brachah without repeating “Borchu” (שם ).
39. Chazan who returns the sefer Torah. On a Shabbos that three sefarim are taken out, the chazan should say יהללו holding the third sefer (שער אפרים שער י' סמ"א ). If he mistakenly took the first or second one, he should not exchange it for the third (שם ).
Two Sifrei Torah – Rosh Chodesh and Chanukah
40. Two sifrei Torah. When Rosh Chodesh falls on one of the weekdays of Chanukah [this year on Sunday of Parshas Vayigash], two sifrei Torah are brought out. The first one is for Rosh Chodesh and divided into three aliyos; the second is for Chanukah and leined in one aliyah (שו"ע סי' תרפ"ד ס"ג ).
41. Mistakenly made four aliyos for first sefer. If they leined Revi’i of the Rosh Chodesh leining but had not brought out the second sefer, they do not need to lein anything else. If they had brought out the second sefer, they must add a fifth aliyah to lein the parshah of Chanukah from it followed by Kaddish since it would be disrespectful to put it away without leining from it (מ"ב סקט"ז ).
Mistakenly Leined Parshah of Chanukah First
42. If they mistakenly put the Chanukah sefer on the bimah first, the halachah is the same as that of Shabbos Rosh Chodesh Chanukah (above, 28). I.e., if the oleh did not make the brachah, they can close that sefer and lein the parshah of Rosh Chodesh from the other sefer. This is not disrespectful to the sefer Torah since they will soon lein from the Chanukah sefer (ביאה"ל ).
43. If the oleh already said “Boruch atah Hashem” of the brachah, he should finish it and they should read the entire Chanukah leining for Kohein. The rest of the aliyos should be from the Rosh Chodesh sefer (ט"ז, ביאה"ל, ודלא כרמ"א שם ).
44. If they leined the parshah of Chanukah until “מלאה קטורת ” for Kohein and they only realized their mistake after the Kohein’s brachah after his aliyah, it is preferable that the first three aliyos be from the parshah of Chanukah and Revi’i from the parshah of Rosh Chodesh (שו"ת חלקת יעקב ח"א סי' ק' ).
