R’ Yitzchak ben R’ Yosef, in mitzvah 280 of his work the Sefer Mitzvat Katan (Smak), explains that there is a mitzvah from the Torah to light Chanukah candles. R’ Yitzchak also connects this requirement of lighting candles to the mitzvah of reciting Hallel, which he counts as a separate mitzvah:

להלל בזמנים קבועים דכתיב (דברים י') הוא תהלתך ואמרו רבותינו (ערכין דף י') בארץ ישראל שמונה עשר יום ולילה אחד. ובגולה) עשרים ואחד יום ושתי לילות וכן מי שאירע לו נס כגון ארבע' שצריכין להודות יורדי הים והולכי מדברות וחולה שנתרפא ויוצא מבית האסורין צריך לברך.

ספר מצוות קטן מצוה קמו

To recite Hallel in the appointed times, as it is written, “This is Your praise” (Devarim 10:21). Our Sages said (Arachin 10a), that in the Land of Israel it is said eighteen days (first day of Pesach, Shavuot, Sukkot, Shmini Atzeret,  and Chanukah) and one night (Pesach night), and twenty one days and two nights in the Diaspora. Similarly, one who had a miracle performed for him must bless.

Sefer Mitzvot Katan, Mitzvah 146

This opinion, that the lighting of candles and the recitation of Hallel on Chanukah has a Torah basis was previously rejected by the Rambam in his Book of Mitzvot: he saw it as an impossibility that an event that happened more than 1000 years after the Exodus and the giving of the Torah could generate these new mitzvot as Torah law[1].

Another peculiarity exists in R’ Yitzchak’s presentation of the mitzvah of Hallel: What is the similarity between reciting Hallel at the appointed times, and reciting birkat hagomel after Hashem, in his infinite mercy, performed a miracle on behalf of an individual?

It would seem that the answer to these two questions lies in the complete verse quoted by the Smak himself:

הוא תהלתך והוא אלהיך אשר עשה אתך את הגדלת ואת הנוראת האלה אשר ראו עיניך:

דברים י:כא

He is your praise and He is your G-d, Who did for you these great and awesome things that your eyes saw.

Dvarim 10:21

If this verse is the source of the mitzvah of Hallel, the connection between reciting Hallel on the three festivals and Chanukah, as well as at a time when a miracle was performed on our behalf is self-evident: each of the three festivals commemorates a unique miracle performed on our behalf during the Exodus and our journey to the Holy Land of Israel: the Exodus, the giving of the Torah, and the Clouds of Glory.[2] Similarly, Chanukah is also a celebration of the miracle of our redemption: “And for the miracles…which You performed for our forefathers… and you delivered the strong into the hands of the weak…”[3]

According to this reading of the verse, it is clear why the Smak counted the recitation of Hallel on Chanukah as a positive mitzvah: Whenever we, as individuals or as a nation, are miraculously brought from despair to deliverance we must express gratitude to our Redeemer through Hallel. 

[1] The Ramban, in his commentary on the Rambam’s work, offers two possible justifications for a possible Torah law of reciting Hallel according to the Behag. However, neither of these reasons would apply to its recitation on Chanukah.

[2] There is a dispute among the decisors if there is a requirement to say Hallel on Rosh Hashanah and Yom Kippur which is superseded by the fact that it is inappropriate to recite Hallel while standing in judgement, or if there is no requirement whatsoever. According to the first view, the miracle of national atonement on the first Yom Kippur is clear; however, it is unclear to this author what would create a requirement for Hallel on Rosh Hashanah.

[3] On two other celebrations of national redemption we do not recite Hallel: the last day of Pesach, and Purim. Both are addressed in Masechet Megillah: regarding the last day of Pesach, Hashem responds to the angels: “My creatures are drowning in the sea, and you want to say shira?” (10b); regarding Purim, the Megilla’s reading “is Hallel” (14a).