Even though it is a Mitzvas Aseh SheHaZman Grama, the gemara (Shabbos 23a) says that women are obligated in the Mitzva of Ner Chanuka since they were part of the miracle. What about Krias Hallel, are they obligated to recite it on Chanuka?Rav Vosner (Shevet HaLevi 1:205 683) brings from the Sdei Chemed that one gadol had a dilemma and it is seems from the Rambam that women are patur from Hallel as they are on Rosh Chodesh.
However Rav Vosner says that it seems from Tosfos (Succah 38a Mi) that they must say Hallel on Chanuka. Tosfos says that although women are patur from Hallel on Succos they are chayav to say Hallel on Pesach night. Tosfos’s reason is that they are obligated to drink the Four Kosos, and the whole point of the kosos is to say Hallel on a Kos.
The reason why Pesach is different, says Tosfos, is because the reason we say it is to celebrate the Nes, which women were part of. If so then it is also possible to say that the Hallel on Chanuka is to celebrate the Nes and therefore women are obligated to say Hallel just like they are obligated to light candles.