Can one fulfill the chiyuv of pirsumay nisa for neiros chanukah via Skype (for example could somoene in the US Skype with someone in Israel if there is no one awake in the middle of the night)?
According to several authorities even somebody lighting (very) late can still light with a berachah. Skype doesn’t appear to make much of a difference, but it doesn’t do any harm, and it will add some pirsum of the nes.
According to the initial enactment, the concept of pirsuma nisa is specifically for the members of the public domain, who must see the candles from the window or the entrance.
In this sense, one has to abide by the gedarim (the parameters) that Chazal enacted. For instance, even without Skype, I could theoretically invite a number of people to stand outside at 3:00am, while I light the Chanukah candles. This doesn’t help, because it is past the time of tichleh regel min ha-shuk (the time that there are people outside), and the fact that I have invited passers by to see the candles is not relevant.
The same will apply to Skype.
However, nowadays, some have the custom of lighting inside, and the pirsum ha-nes is fulfilled by the members of the household. Moreover, according to some authorities even those who light outside, can light inside if the time has been missed (see Mishnah Berurah 572:9, 11).
The Mishnah Berurah (672:11) writes that where one’s wife/children are awake, one can recite a blessing upon lighting even beyond the time of tichleh regel min ha-shuk. For somebody lighting alone, the Mishnah Berurah maintains that one does not recite a berachah (at 2:00 in the morning), but others, including the Iggros Moshe (Orach Chaim Vol. 4, no. 105) writes that one does recite a berachah (see Shaar Hatzion 17, citing from Chemed Moshe).
The question now is whether Skype, or a video link-up, can help in this sense: I wish to recite a berachah at 2:00 in the morning, even according to the Mishnah Berurah, but don’t have anybody around to light before. Can a video link help?
Poskim have discussed video links in terms of eidus (testimony), and in terms of other halachic questions, and the general consensus is that a video link cannot be considered as if the person is actually there. However, for Chanukah, there does not appear to be a need for the person to actually be there, and only for there to be a pirsum.
Yet, it is hard to rely on this alone, because the enactment to light at home means to publicize the miracle to the household, and not to people outside the home — and certainly not to people in a different town and state.
However, somebody who is making a berachah even though he is lighting alone (based on the poskim above), won’t do any harm by adding a Skype/video connection, and adding extra pirsum ha-nes to others.