This week, we take three Sifrei Torah out of the Ark. One for Mikeitz, one for the Chanuka reading of the Nesi’im, and one for Rosh Chodesh. Though we could have used the same Torah for both Chanuka and Rosh Chodesh, since they are close to each other, it is considered disrespectful to make the tzibbur wait. Therefore, we take out a third Torah.
Many say that on such a day, it is an auspicious time to daven. This is a wide-spread segula, though its origins are not so clear.
There is a posuk which says the gates of the “inner chamber” are closed all week, but open on Shabbos and Rosh Chodesh. Since this week is both, that implies an even greater opportunity for prayers to ascend to Hashem’s inner sanctum.
Whenever the ark is open is an auspicious time to daven, and since we take out three Torahs, the ark is open longer, giving us more time to pray. This may be part of the source.
Regardless, one should take the opportunity to daven when the three Torahs are taken out, and, enhanced by the spiritual light of Chanuka, the tefilos should be very powerful!
Of course, when you thank Hashem, you should immediately ask for more. On this holiday of hallel and hoda’ah, say “Thank You, Hashem!” then go ahead and ask for the gifts you need.