Halacha requires reciting the full Hallel on each of the eight days of Chanukah. When during the day may the Hallel be recited?
Based upon the verse, "From the rising of the sun until it sets, Hashem's Name is praised" (Tehillim 113:3), the Sages teach that one may recite Hallel from the point of Netz Ha'chama (sunrise) until Sheki'a (sunset). If a person recited Hallel within 72 or so minutes before sunrise, he has fulfilled his obligation "Be'di'avad" (after the fact).
If a person did not recite Hallel throughout the day and he has the opportunity to do so during the period of Bein Ha'shemashot (13.5 minutes after sundown), should he recite Hallel at that point?
The status of the Bein Ha'shemashot period as belonging to the day or the night is one of Safeik, or Halachic uncertainty. Seemingly, in light of the ruling of the Rambam (Rabbi Moshe Ben Maimon, Spain-Egypt, 1135-1204) that reciting Hallel is a Rabbinic, rather than Biblical, obligation, we should apply here the rule of "Safeik De'Rabbanan Le'kula," allowing one to act leniently in situations of doubt concerning laws ordained by the Rabbis. Thus, one might argue, a person in this situation should not be required to recite Hallel, as he may assume that Bein Ha'shemashot belongs to the nighttime at which point he can no longer recite Hallel. However, Chacham Ovadia Yosef rules in his work Chazon Ovadia (Laws of Chanukah, p. 231) that since reciting Hallel does not entail particular difficulty or inconvenience, one should recite Hallel during Bein Ha'shemashot in this case, though without a Beracha.
Many books record the custom to add each morning during Chanukah the chapter of Tehillim "Mizmor Shir Chanukat Ha'bayit Le'David Aromimcha Hashem..." (chapter 30) after the Shir Shel Yom. Now we recite this chapter each morning throughout the year, as well, before "Hashem Melech," only we begin with the verse "Aromimcha Hashem." Is it appropriate during Chanukah to begin with "Mizmor Shir Chanukat Ha'bayit" when reciting this chapter before "Hashem Melech"?
Chacham Ovadia writes in Chazon Ovadia (ibid.) that one does not begin with the verse "Mizmor Shir" when reciting this chapter before "Hashem Melech" during Chanukah, since he will in any event recite this chapter in honor of Chanukah after the Shir Shel Yom. One rather recites "Aromimcha Hashem" as usual, and then adds the entire chapter of "Mizmor Shir Chanukat Ha'bayit" later, after the Shir Shel Yom.
Summary: One may recite Hallel during Chanukah anytime during the day from sunrise to sunset; if one recited Hallel within 72 or so minutes before sunrise, he has fulfilled his obligation. If one realized within 13.5 minutes after sundown that he had not recited Hallel that day, he should recite it at that point without a Beracha. It is customary to add the paragraph of "Mizmor Shir Chanukat Ha'bayit" after the Shir Shel Yom each morning during Chanukah. We recite "Aromimcha" before "Hashem Melech" as usual during Chanukah.
