There are different opinions among the Rishonim[1] and Achronim[2] regarding the appropriate time to light Hannukah candles.
Sepharadim custom follows the Shulhan Aruh[3] which states, "Hannukah candles are not lit before sunset, but rather with the end of sunset. One does not light later or earlier", meaning the time to light the candles is at the time when the stars come out[4] (around 5:15pm in New Jersey).
Some Ashkenazim have the custom of following the Shulhan Aruh and light Hannukah candles when the stars come out. Others follow the opinion of the Vilna Gaon[5] and light Hannukah candles at sunset (around 4:30pm in New Jersey). The Mishnah Berurah[6] writes that those who light candles at sunset should still put enough oil in the candles so that they will remain lit at least a half hour after the stars come out, similar to how we light Hannukah candles on Friday evening before Shabbat.
The Kabbalists follow the opinon of the Simhat Cohen[7]. The Simhat Cohen brings the custom of the people of Bet El who after praying Minha would go to their homes and light their Hannukah candles while reciting the special prayer of the Rashash before sunset. Then they would go back to pray Arvit after the stars come out. Rav Ovadia Hedaya[8] concurs with this custom, stating its origin is from the Pri Etz Hayim. However, we need to investigate this matter further as this custom was not brought down by the Ben Ish Hai or the Kaf Ha’Hayim.
If in extenuating circumstances, one is required to leave their house before sunset, they may light their Hannukah candles with a blessing as early as after Plag Ha’Minha, which is one and a quarter Halachic hour before the stars come out. One who does so must again make sure to have enough oil or wax in the menorah for the lights to burn until half an hour after the stars come out.
One who is unable to light Hannukah candles at the optimum time, may light within 30 minutes of that time. If a half hour past and they still have not lit the candles, they may light candles at any point the entire night with a blessing, up to a half hour before dawn. It is preferable to wake one or two members of the household to be present while lighting in order to publicize the miracle.
Rav Ovadiya in his book Yehave Daat[9] was asked regarding a soldier who is unable to light the Hannukah candles when the stars come out because of security reasons and wanted to light the candles with a blessing before sunset, and to put out the candles as soon as night falls. He answered that one could rely on the opinions that says if one lights from Plag Ha’Minha and on he could recite a blessing. However, if he plans on putting out the candles at nightfall, because of security reasons, he cannot say a blessing on that lighting, since the candles must be lit at least a half hour after the stars come out, and therefore he would be saying a blessing in vain. Similarly, one may not recite a blessing when lighting candles after dawn.
In conclusion:
Sepharadim light Hannukah candles when the stars come out (around 5:15pm).
Ashkenazim either follow the Shulhan Aruh and light when the starts come out (around 5:15pm) or the GR’’A and light at sunset (around 4:30pm.)
Mekubalim light Hannukah candles before sunset.
In extenuating circumstances, one can light with a blessing from Plag Ha’Minha.
One who cannot light at the optimal time can light the entire night up until a half hour before dawn.
One who plans one extinguishing his candles before night fall cannot say a blessing with candle lighting.
One cannot say a blessing when lighting after dawn.
Footnotes
leading rabbis who were deciders of Jewish law and lived between 1050 and 1500.
leading rabbis who were deciders of Jewish law living from the 16th century to the present.
Orach Hayim Siman 672 seif 1.
Mishnah Berurah seif katan 1; Ben Ish Hai, Vayeshev 1:7; Kaf Ha’Hayim seif katan 2; Hazon Ovadiya Hannukah pg. 62; Ohr LeTziyon, vol 4, 43:1.
Maaseh Rav 235
Mishnah Berurah seif katan 1
End of siman 113
Shalom VeTzedek end of siman 46
Part 7, siman 84