Gemara

A Ner during the day is useless.

Shabbos 23b: Rav Yosef's wife used to light late.

Rav Yosef: A Beraisa teaches "Lo Yamish Amud he'Anan Yomam v'Amud ha'Esh Laylah Lifnei ha'Am" - the fire came before the cloud left (towards evening. This teaches that it is proper to light before dark.) The fire would not leave until the cloud came (in the morning).

His wife: If so, I will light early in the day!

(An elder - Beraisa): One may not light too early, nor too late.

Beitzah 22a (Rav Yehudah): Kinva is permitted.

Rishonim

Rambam (Hilchos Chanukah 4:5): We do not light Ner Chanukah before Sheki'ah, rather, with the end of Shki'ah. We do not light earlier or later.

Magid Mishneh: Shabbos 23b says that one may not light too early or too late. The Rambam understands that this refers (only) to Ner Chanukah.

Rosh (Beitzah 2:18): Kinva is like the Aruch says, after the Ner extinguished, we cut the burnt end of the wick. The Chidush is this is not making a Kli, so it will be easy to light. This is only if he wants to light it that night.

Mordechai (Shabbos 294): In summer, one may light in the house and eat in the Chatzer, and he will have daylight. This is because Ner Shabbos is just so people will not stumble on wood or rocks, and he has much daylight (so he will not stumble, i.e. there is Shalom Bayis). A Gadol enacted like this in Germaiza. R. Meshulam would not bless on Ner Shabbos, because Menachos 42b says that we do not bless on a Mitzvah if it is not finished through our action. Here, it is finished only when we eat. The Ri says that we bless. The Mitzvah is finished, for it enables us to see in the house and take Kelim to the table. If one lit during the day, he need not extinguish it and relight it. R. Tam says that he must, for the Gemara said that one may not light early or late.

Question: The Mitzvah of Ner Shabbos is primarily in the house, for Shalom Bayis. However, we light outside during the day and bless, even though Shalom Bayis does not apply, for a Ner during the day is useless. Sometimes we light in the house and eat in the Chatzer. Maharam did so. Sometimes the Neros do not last until night. We can justify the custom. Since Shalom Bayis applies in the house, we do not distinguish between winter and summer (so one may light in the house and bless even in summer, even if he eats then in the Chatzer). However, one may not bless on lighting in the Beis ha'Keneses. There, we light only to honor the place!

Answer (Maharil Teshuvah 53): If the women light their own Neros or add to the Neros of the Beis ha'Keneses, we can justify this. The addition is considered Shalom Bayis, even though there were enough Neros in the Beis ha'Keneses. This is like two or three Ba'alei ha'Bayis eating in one place. Each blesses on his candelabra, even though there is already much light. Or Zaru'a questioned this, but some have the custom. I say that extra light gives more Shalom Bayis and Simchah. We light Neros in the Beis ha'Keneses on Yom Tov (during the day), even though a Ner during the day is useless. Maharam said that this is not l'Vatalah, for we enjoy the extra Neros, and it is considered a need of the day and a Mitzvah. Even though Semag (Magihah - this is not in Semag, but the Mordechai Yoma 728 and Agur bring it) says that we do not bless on any Ner not for the sake of eating, unlike all his Rebbeyim, we do not hold like him (Semag). Many Gedolim say that we light in the house and eat in the Chatzer. There, the Ner helps for needs of the meal. Here also, perhaps in the Beis ha'Keneses one will use the Neros for needs of the meal.

Maharil: The Agur says that if one lights in corners of the house and eats in the Chatzer, if the Neros do not burn until the night, the Berachah is l'Vatalah. People denounce the custom to do so. I say that it was somewhat dark where they lit, like it often gets dark in rooms towards evening, and he uses the light for something. However, I find no Heter at Chupos when women light early and the Neros do not last until night, unless they light in cellars where it is dark.

Poskim

Shulchan Aruch (OC 263:9): If one lights in corners of the house and eats in the Chatzer, if the Neros do not burn until the night, the Berachah is l'Vatalah.

Levush (10): The primary reason for Neros Shabbos is to benefit from them, i.e. after dark. A Ner during the day is useless. The primary Hadlakah on which we bless is on the table on which they eat.

Mishnah Berurah (40): The Shulchan Aruch connotes that if he eats in the house, even if the Neros do not burn until dark, it is permitted. This is because there is Simchah and benefit to eat in front of Neros. The ideal Mitzvah is to have Neros that will burn until dark.

Kaf ha'Chayim (59): The Neros should burn until dark, so there will be Shalom Bayis when he enters the house after the meal.

Magen Avraham (17): If it was slightly dark where he was eating, and he uses the Ner for something, perhaps there is no Isur.

Mishnah Berurah (41): If he uses the Ner for some need of the meal, even if he ate in the Chatzer, there is no Isur.

Shulchan Aruch (OC 514:4): If a Ner extinguished on Yom Tov and one wants to light it the same day, he may cut the end of the wick in order that it will be easy to light.

Beis Yosef (DH Ner): This is only when he will light it that night, i.e. that night or the same day. One may not fix to on Yom Tov for the next day, and all the more so not for a Yom Chol.

Bach (5): The Tur permits Kinva only if he intends to light it at night. He excludes the next night or Yom Tov Sheni. He mentioned at night, for this is a normal case. There is no need to light during the day. A Ner during the day is useless!

Shulchan Aruch (672:1): We do not light Ner Chanukah before Sheki'ah, rather, with the end of Shki'ah. We do not light earlier or later. Some say that if one is busy, he may light earlier, from Plag ha'Minchah (one and a quarter hours before the end of the day), as long as he puts enough oil to burn until the last people cease from the market.

Bach (672:1): The Mitzvah of Ner Chanukah is from Sheki'ah until people cease walking in the market. The Tur and Mordechai explain that we refer to the end of Sheki'ah, for a Ner during the day is useless!

Magen Avraham (1): If one lit during the day, we do not benefit from it and one may not bless on it. Chachamim said that one may not bless on a Ner unless he benefits from it.

Levush (2): If one did not light at night, he does not light the next day. A Ner during the day is useless; there is no publicity to the miracle.

Gra (DH v'Yesh): We learn from Havdalah (that one may not bless on a Ner unless he benefits from it).

Bi'ur Halachah (DH v'Lo): Most Poskim (R. Chananel, Rashi, Tosfos, the Rosh, R. Yonah, Mordechai) explain that Shabbos 23b discusses Ner Shabbos. If so, there is no source for the Rambam's law. The Tur brings this regarding Shabbos. Why does the Shulchan Aruch bring it regarding Shabbos and Chanukah? Perhaps the Tur and Rambam learn from reasoning (that one may not light Ner Chanukah early). There is no publicity to the miracle, for a Ner during the day is useless. However, the Shulchan Aruch adopted the words of the Tur and Mordechai, that one lights at the end of Shki'ah, which is Tzeis ha'Kochavim. If one lights slightly earlier, e.g. 15 minutes earlier, this is Bein ha'Shemashos. There is a Heker then (the Ner is seen)! The Shulchan Aruch says that one may not light Ner Shabbos too early, for then it is not evident that it is for Kevod Shabbos. Even so, one must light before Bein ha'Shemashos. We must say that 'one may not light (Ner Shabbos) too early' means while much time remains in the day (before Bein ha'Shemashos). The same applies to Ner Chanukah. There is no problem to light 15 or even 30 minutes before Tzeis ha'Kochavim. The Tur said 'from the end of Shki'ah', but did not say 'one may not light earlier. The Rambam said 'one may not light earlier', but he said only 'from Shki'ah'. He did not say 'from the end of Shki'ah'. One may light before Shki'ah, but not much before. The Shulchan Aruch wrote both 'from the end of Shki'ah', and 'one may not light earlier.' This requires investigation.

Levush (564:1): If one sees moonlight on the ground, surely it is after Shkia'h. One may eat (after a Ta'anis) even if he does not see stars. The moonlight covers them, just like they cannot be seen during the day due to sunlight, like we say that a Ner during the day is useless.