Beginning of new Hebrew month of Tevet. Tevet is the 10th month of the Hebrew year. Corresponds to December or January on the Gregorian calendar.
Ezekiel 46:3New International Version (NIV)
3 On the Sabbaths and New Moons the people of the land are to worship in the presence of the Lord at the entrance of that gateway.
The New Moon has nothing to do with pagan worship, it has everything to do with what is required by the Torah.
Hanukkah (Hebrew: חֲנֻכָּה, usually spelled חנוכה pronounced [χanuˈka] in Modern Hebrew, also romanized as Chanukah or Chanuka), also known as the Festival of Lights, is an eight-day Jewish holiday commemorating the rededication of the Holy Temple (the Second Temple) in Jerusalem at the time of the Maccabean Revolt of the 2nd century BCE. Hanukkah is observed for eight nights and days, starting on the 25th day of Kislev according to the Hebrew calendar, which may occur at any time from late November to late December in the Gregorian calendar.