The mitzvah of Chanukah lights is a unique one. It is not incumbent upon the individual, but rather on the household: "One candle for a man and his household." Why did Chazal define this mitzvah as a household obligation and not as an individual obligation? The mehadrin (more stringent observers) even light a candle for every member of their household. What is the connection between the family and the miracle of Chanukah?

If we study the Midrash we will discover that most of the Greeks' decrees related to the family. The Midrash Ma'aseh Chanukah (Otzar Midrashim, Eisenstein) relates:

In the days of the Greeks there was a conspiracy against Am Yisrael. They said: "Let us make decrees against them until they shall forsake their G-d and believe in our idolatry.

They got up and decreed: Any Jewish person who places a lock or frame on his opening shall be stabbed with a sword. All this for what? So that Am Yisrael would have no respect and no modesty. Since any house without a door has no respect and no modesty, and anyone who wishes to enter may enter during the day and during the night. When Am Yisrael saw this, they decided to remove all the doors from their homes, and could no longer cohabit. They stood and decreed that any person whose wife goes to the mikveh shall be stabbed with a sword...

They stood and decreed a bitter and vile decree that a bride shall enter on her first night of marriage only with the officer. When Am Yisrael heard this, their hands weakened and their strength left them and they ceased betrothing.

The common denominator of all these decrees is the aim to destroy the Jewish home, the family cell. First they picked on the house, a person's private domain, and made it a public domain. Then they attacked family purity, and later betrothing and marriage.

Therefore, when the Chashmonaim overcame the Greeks the family triumph was emphasized, and they established: "One candle for a man and his household." The Rambam rules (Hilchot Chanukah 6:10): "The mitzvah is that each and every household lights one candle, whether if the members of the household are numerous, and whether there is only one person." The pirsumei nisa (advertisement of the miracle) is only through the household. Similarly, the halacha is: "At the entrance to his house on the outside." Rashi's opinion is that the mitzvah is at the entrance to the house, and not at the entrance of the courtyard that faces the public domain, because the obligation is on the house. There is an emphasis on the entrance of the house because the entire victory was about maintaining the family cell that is within the house.

Rav Kook adds (Ein Ayah, Shabbat 23a):

The Greeks in their decrees wanted to take from Am Yisrael the Jewish life, which is built on the roots of the Torah, and one of its foundations is to set modesty and purity as the main goal of family life.

This outlook on life contrasts the Greek culture, which viewed it as an enemy. They placed the joy of life and its physical and fantasized pleasures at the summit of their existence, and because of this the Greeks hated the Torah greatly. Therefore, in order to emphasize how much the Jewish family held a part in the victory over the Greeks, it was decided that the basic obligation in Chanukah would be, "One candle for a man and his household." 

This is what the Shabbat candle is about. The entire point of lighting the candle is to increase the peace between a man and his wife and to maintain the family cell. Therefore the Rambam ends the laws of Chanukah with a subject that relates to the laws of Shabbat:

If a person had before him [the choice of] his house's candle or the Chanukah candle, or his house's candle and the kiddush of the day, his house's candle comes first because of the peace of his household, as the [Divine] Name is erased in order to create peace between a man and his wife. [This refers to the law of a sotah, where the kohen erases Hashem's name in the water in order to test her and resolve the husband's suspicions.] Peace is a great ideal, as the entire Torah was given in order to promote peace in the world, as it says: "Its ways are ways of pleasantness and all its pathways are peace." (Mishlei 3:17)

This ruling in the Rambam is very puzzling. Only the beginning of his words relates to the laws of Chanukah, while the rest relates to the laws of Shabbat. Why did the Rambam see fit to conclude the laws of Chanukah with the subject of household peace? It is because this is what Chanukah is really about: "One candle for a man and his household," which is based on the Shabbat candle. Therefore, when there is a choice between the Shabbat candle and the Chanukah candle – the Shabbat candle takes priority, because the Shabbat candle is the basis for the Chanukah candle.

Therefore, on Chanukah the entire family gathers around the Chanukah candles, and it is forbidden to do any work during that time, because the candle lighting is the time when the family cell is united. Peace is a great ideal, as the entire Torah was given in order to promote peace in the world, as it says: "Its ways are ways of pleasantness and all its pathways are peace."