The Gemara in shabbat 22a teaches “Raba proclaimed, the Chanukah candle should be lit within a tefach of the entrance.” It then clarifies the matter further asking: “Where precisely should the candle be placed?” In response to this question two opinions are presented. Rav Acha son of Rava states that the candles should be placed on the right, while Rav Shmuel of Diftey is of the opinion that it is more appropriate to place the candles on the left side. Rav Acha’s opinion is based on the general view of Halacha that right is symbolic of importance and is therefore the appropriate place for an object of Mitzvah. Rashi explains that “right” and “left” pertain to the right or left of a person entering the house. This understanding is based on the conclusion of the Gemara, which accepts the opinion of Rav Shemuel of Diftey, to light on the left, so when entering the house the Mezuza is on the right and Chanukah candles on the left, creating an encirclement of Mitzvot.
In the Shiboley Haleket we find this Halacha stated in a particularly colorful way. “Halacha is that the candles be placed on the left so that the Mezuzah be on the right, the Chanukah candle on the left and the Baal Habyit stands between them wearing Tzitzit.”
Practically, where Chanukah candles are lit outside, the candles should be placed on the left side opposite the Mezuzah. When lighting in a place with no Mezuzah, as at the entrance of a yard that has no doorway, the Chanukah candles should be placed on the right of the entrance. (Shulchan Aruch OC 671/7)
Where the candles are lit indoors Rav Yosef Karo in the Shulchan Aruch (OC671/5) states that the ideal location would be at a window. This seems to indicate that in such circumstances there is no need to light near the door and the Mezuzah plays no part in determining where to place the Chanukah candles. The Ramah states that since we light indoors and it is not notable to those on the outside there is no need to light at the doorway. But, says the Rama, the costume, none the less, is to light near the door (on the inside) as in the past. Consequently, one should light the Chanukah candles to the left of the door across from the Mezuzah.
The Rama’s words are interpreted by the later Poskim as saying, that when lighting indoors, where there is no possibility for the candles to be seen by people on the street, then the proper costume is to light near the door. Yet, where possible it is preferable to light near a window, as stated by the Shulchan Aruch, so as to create publicity for the candle lighting. Rav Moshe Feinstein notes, the Mezuzah is not a halachic requirement, but rather a directive of location in the event the Mitzvah can be fulfilled equally on both sides of the doorway.
In one particular situation Mezuzah does play a part in the halachic definition of where candles should be lit. Discussing the question of lighting Chanukah candles in a Beit Knesset, Rabbi Avraham son of Natan Hayarchi in his Sefer Hamanhig, claims that it is clear there is no requirement to light in a Beit Knesset, since it is not a residential building. Explaining his position, the Manhig claims, that since the requirement is to light in a person’s home “Ner Ish Uveito”, and since the Gemara speaks of lighting across from the Mezuzah, it is clear that only a house requiring a Mezuzah, namely a residential structure, requires the lighting of candles. Therefore, concludes the Manhig, lighting in a Beit Knesset can only be considered a custom not a halachic requirement.