Hilchos Chanukah - Laws of Chanukah
Women are obligated to light Chanukah candles because they were also part of the miracle. Hashem's salvation came about through Yehudis bas Yochanan, Kohein Gadol when she cut the head off a chief enemy.
--Shulchan Aruch 675:3/Mishna Berurah 10

A women can light candles on behalf of her family. A man can designate his wife as his shaliach (agent) to perform this Mitzvah as long as he is present when she makes the Brocha. Nevertheless, the Minhag is that the husband lights and the wife fufills her obligation through him. However, if the husband is not home, the wife should light and make the Brochos.

--Mishna Berurah (SA 675), sub-paragraph 9