CHANUKAH aLWAYS hAS a sHABBOS IN ITS mIDST
Not only will Chanukah always coincide with a Rosh Chodesh (Tevet) and at least one Shabbos, but because Chanukah is eight days long, there will always be the possibility that a baby boy born on the first day of Chanukah will have his bris milah on the eighth day of Chanukah!
Chanukah coincides with these three mitzvot in particular because the Yevanim specifically targeted these three mitzvot for eradication (see 4.24). By performing these three mitzvos specifically on Chanukah, we highlight the fact that, not only were the Yevanim not successful, but in addition, while they and their decrees have faded into history, am Yisrael chai! The Jewish people and the Torah are still here and thriving, baruch Hashem!
(See Bnei Yissaschar, Maamarei Chodshei Kislev-Teves 4:88, 97; A.P.S.)
Cited in “Inside Chanukah” by Aryeh Pinchas Strickoff. Published by Feldheim Publishers, New YorK