Question: Since women are obligated to light Chanukah candles, does this mean that they are likewise obligated to recite the Hallel every morning of Chanukah as well?
Answer: Women are exempt from all positive, time-bound Mitzvot, such as eating in the Sukkah, taking the Lulav, and hearing the Shofar (as opposed to negative, time-bound commandments, such as eating on Yom Kippur or performing forbidden works on Shabbat, which they certainly are obligated to observe). There are certain Mitzvot which are exceptions to this rule but this is nevertheless the general rule.
Based on this, it seems that women should be exempt from lighting Chanukah candles, for this too is a positive, time-bound Mitzvah since it only applies on Chanukah.
Nevertheless, our Sages said that women are, in fact, obligated in the Mitzvah of lighting Chanukah candles, for when our Sages instituted this Mitzvah, this was done in order to publicize the miracle that Hashem performed for our ancestors in those days. Since women were included in this miracle, they were not excluded from the enactment of our Sages and they were likewise obligated to light Chanukah candles.
If so, it seems that the same should apply regarding the recitation of the Hallel throughout Chanukah, for reciting Hallel during the days of Chanukah is likewise a rabbinic enactment in order to publicize the miracle of Chanukah and to thank Hashem for it. Since women were included in this miracle, it seems that they should likewise be obligated to recite Hallel every day of Chanukah with a blessing.
Nevertheless, the Rambam and other Poskim write that women are exempt from reciting the Hallel on Chanukah. Maran Rabbeinu Ovadia Yosef zt”l explains this matter beautifully and writes that although women were included in the miracle of Chanukah, our Sages nonetheless did not wish to obligate them in the Mitzvah of reciting the Hallel, for there is a great distinction between the Mitzvah of lighting Chanukah candles and the Mitzvah of reciting the Hallel. Since lighting the Chanukah candles causes the miracle to be publicized in a grand manner for all passerby to see who will then remember the miracle Hashem performed for our forefathers, our Sages decided that it is correct that women be obligated to perform this Mitzvah as well. On the other hand, reciting the Hallel on Chanukah is strictly between man and his Creator and does not constitute as grand a publicization of the miracle and therefore, our Sages did not want to differentiate between the laws regarding reciting Hallel on Chanukah and reciting Hallel on any other holiday and they therefore exempt women from reciting Hallel on Chanukah (see Chazon Ovadia-Chanukah, page 214).
Summary: According to the law, women are exempt from reciting the Hallel on Chanukah. Nevertheless, women who recite Hallel after praying throughout the days of Chanukah are especially praiseworthy. However, they may not recite a blessing before doing so since they are not obligated to do so.