On each of the eight days of Chanukah, men are obligated to recite the complete Hallel service, with the introductory Beracha, "Baruch Ata…Asher Kideshanu…Ligmor Et Ha'hallel." Women have the option of reciting Hallel as part of the prayer service during Chanukah. However, as Chacham Ovadya Yoseph writes in his work "Yabia Omer" (vol. 6), women reciting Hallel on Chanukah must not recite the Beracha. Since it is questionable whether this Beracha is sanctioned, we apply the rule of Safek Berachot Le'hakel – meaning, that we refrain from reciting a Beracha when uncertainty exists concerning its obligation. Thus, while it is certainly appropriate for women to recite Hallel on Chanukah, they must ensure to omit the introductory Beracha.
The Ben Ish Chai (Rabbi Yosef Chaim of Baghdad, 1835-1909) emphasizes that one should recite Hallel on Chanukah with particular concentration and joy. He notes that even on Pesach we do not recite the complete Hallel service throughout the festival, and it is thus a rare opportunity we have on Chanukah to recite the full Hallel, and we should therefore do so with sincere emotion.
On Rosh Chodesh Tevet, which occurs during Chanukah, there is a custom to light an extra candle in memory of Rabbi Meir Ba'al Ha'ness. Additionally, the Ben Ish Chai writes that the double festivity of Rosh Chodesh Tevet – as both Rosh Chodesh and a day of Chanukah – warrants an extra dimension of celebration, and one should therefore eat a festive meal on the day of Rosh Chodesh Tevet.
Summary: One must recite the complete Hallel service on each of the eight days of Chanukah with its introductory blessing, and with particular joy and sincerity. Women certainly may recite Hallel, but they must omit the introductory blessing. On Rosh Chodesh Tevet, some have the practice to light an extra candle in memory of Rabbi Meir Ba'al Ha'ness; furthermore, it is appropriate to conduct a festive meal on Rosh Chodesh Tevet in honor of the double celebration of this day.
