The month of Kislev is of Babylonian origin, like all the months in the Jewish calendar today. In the Bible, Kislev does not have a name but is referred to as the ninth month because in the Bible the months are numbered, starting from the month of Nissan. Kislev is most famous for having the festival of Chanukah in it but it also has significance in the Bible.
Firstly, the first ever rainbow to appear in the world appeared after the Flood in none other than the month of Kislev. It is recorded in the book of Genesis/Bereishit, “And G-s Said: ‘This is the sign of the covenant which I set between Me and you and between every living being that is with you, for eternal generations. I have placed my bow in the cloud and it shall be a sign of a covenant between Me and the earth.’ “This is the sign of the covenant”-G-d Showed Noah the bow and said to him, “This is the sign of which I spoke.” (Genesis Chapter Nine)
Rosh Chodesh Kislev- the first day of Kislev and sometimes also the last day of the previous month Cheshvan- is either one or two days long. Cheshvan either has twenty-nine or thirty days. When Cheshvan has twenty-nine days, Rosh Chodesh Kislev consists of just one day which is the first day of Kislev. When Cheshvan has thirty days, Rosh Chodesh Kislev has two days- the first day is the thirtieth day of Cheshvan and the second day is the first day of Kislev.
From the time of the Hasmoneans the Jewish Supreme Court would sanctify the month through witnesses testimonies of seeing the New Moon. Once it was clarified that the witnesses had indeed spotted the new moon, messengers would be sent out from the Jewish Supreme Court to locations all over the land of Israel to make it public knowledge that the new month had been sanctified.
This occurred only during months that contained festivals so that people would know when to celebrate the festival. Therefore, when Kislev was sanctified messengers were sent out so that those living outside of Jerusalem would know when the festival of Chanukah was to begin. Chanukah is a festival of Rabbinic origin that is only mentioned indirectly in the Torah. Nonetheless, especially in recent decades it has become a more central festival, with Jewish people taking pride in the message of religious freedom that it contains.