Zos Chanukah, the eighth day of Chanukah, is said to be a special time for Tefillah, and according to the Bnei Yissoschar it is a time of Gmar Din for the Tfillos of the Yomim Nora’im.
The Rebbe of Ruzin is quoted as saying that the Tfillos of a simple person on Zos Chanukah is comparable to the Tefillos of Tzadikim on Rosh Hashana and Yom Kippor.