Generally speaking, if a person travels on Hanukah, and his wife remains home, then the wife lights the Hanukah candles at home and the husband fulfills his obligation of Hanukah candles through her lighting. He does not have to light in the place he is visiting.
However, the Shulhan Aruch (Orah Haim 677:3) makes an exception in the case of one who travels to a remote location where there are no Jews. A common contemporary example would be a Jew who travels to the Far East on business during Hanukah, and he thus finds himself in a place where no one is lighting Hanukah candles. In such a case, the Shulhan Aruch writes, one should light Hanukah candles, with the Berachot. A traveler fulfills his obligation with his wife’s lighting back home only if he is in a place where there are Jews lighting Hanukah candles and he thus sees the candles and participates in the Pirsumeh Nisa (publicizing of the miracle). If, however, he is in a place without any Jews, he must light his own candles, even though his wife is lighting at home, and he recites the Berachot over the lighting.
Preferably, in order to satisfy all opinions, a person in such a situation should specifically have in mind not to be covered by his wife’s lighting back home, so that he can recite the Berachot according to all views.
This is the ruling of Hacham Ovadia Yosef, as recorded in Yalkut Yosef (p. 169).
Summary: Although one who travels on Hanukah generally does not have to light Hanukah candles, as he fulfills his obligation through his wife’s lighting at home, if he is in a place with no Jews he should light Hanukah candles, with the Berachot.
