In a sicha delivered on Shabbos Parshas Vayeshev 5750, the Rebbe speaks about the appropriate way to conduct ourselves on this night.
By Anash.org writer
The night of the 24th of December is known as “Nittel Nacht.” On this evening, there is an extra measure of kelipa in the world, due to the events that are commemorated by other nations on this day. As in many communities, minhag Chabad is to refrain from learning Torah from shkiah until chatzos halayla. The reason for this is to avoid adding vitality to the forces of impurity.
The Rebbe relates that the Rebbe Rashab was careful not to learn chassidus, as well as other aspects of his conduct on this night. In a sicha on Shabbos Parshas Veyeshev 5750, the Rebbe said that we learn from this to utilize the time of nittel for practical benefit. It is appropriate to use this time for matters that lead to increased wisdom, such as playing chess, which sharpens the mind. One should also increase in acts of tzedakah and chesed, or use the time to take care of the home. In the sicha, the Rebbe specifically mentions sewing clothing and picturing the Rebbe’s face in your mind.
For this reason, many have the custom to play chess on nittel nacht.
Read more about nittel nacht at chabad.org.