It’s clear from Maran, that ladies are also obligated in the Mitzvah of Ner (lighting) Chanukah as well as the men. And therefore, they also are able to light.
The Chafetz Chayim in his commentary Bi’ur Halacha (Orach Hayim 675:1) writes that it would not be proper for the wife to light when the husband is home, based on the Gemara Berachot 20, that says ‘cursed is the man that lets his wife fulfill for him his Mitzvah.’ The Gemara although says that Rabbi Zera would let his wife light for him, but that was because he was in the Yeshivah and not at home. Since the Mitzvah to light is on the house, and Rabbi Zera couldn’t light since he was away, he therefore was allowed to let his wife light for him.
The Pinei Yehoshua (written by Reb Yaakov Yehoshua Falk Katz, 1680-1755) learns this concept that the Mitzvah of Chanukah is on the house from the language of the Gemara. The Gemara says "Mitzvat Chanukah Ner Ish U’Beto." (The Mitzvah is the lightning by the people of the household.)
I saw an explanation why Ner Chanukah is different, that the obligation ‘so to speak’, is on the house? So the explanation is about one of the decrees of the Greeks which is not so well known. The Greeks made the Jewish people keep their doors open. Some even say that the Greeks actually knocked down their doors. The Greeks did this because they tried to affect and influence the Kidusha (holiness) and the modesty of the Jewish home. When the door is open, everyone could see right through negating modesty, and all the outside influences of the street are able to penetrate. That was the Greek plan. They wanted to compromise the Jewish home. And since it was one of the plans of the Greek to destroy the Bet (house) of Israel, so therefore the Mitzvah is to sanctify the Bet of Israel.
So it’s an obligation on the house. We are coming along and lighting the Menorah in order to try and fix exactly what the Greeks were trying to eradicate from us.
The Halacha, if a man would find himself away out of town on the holiday, and his wife is home, he would appoint his wife, and his wife would light at the proper time, and he and the house would be fulfilling the obligation through his wife. And there is no problem of the curse. (See Torat HaMoadim siman 2:1.)
