Pirsumei Nissa - Igrot Moshe Orach Chaim 4:105.7

This section of the teshuva deals with the question of whether or not pirsumei nisa is meakev the lighting of Chanukah candles, and Rav Moshe uses the same issue with regard to reading Megilla as his source. By Megilla, we rule that pirsumei nisa is a hiddur mitzva, but is not actually meakev the mitzva, and thus a person can read Megilla even if they are alone (Rav Moshe does note that there is a machloket about reading alone if one has the chance to read with a minyan, but we rule that even in that case one can read alone with a bracha). That being the case, Rav Moshe claims that the same is true by Chanukah candles, and thus one can light with a bracha even if he is by himself and even if there is no one else around to see the candles.