It seems to me that the right side is usually given precedence in performing mitzvot. Why is the Chanuka menora lit on the left side of the doorway?
Many people nowadays light inside the house either on a table or in the window. But it is correct that according to the original halacha, and as still practiced by many today, the ideal location to light the Chanuka menora is on the left side of the main, outer doorway into the house.
One reason that’s given in the sources is in order that a person might be encompassed by mitzvoth. By the mezuza whose place is fixed on the right and the menora which is therefore placed on the left. In this way, a person’s goings out and comings in are illuminated by the spiritual and physical light of the mezuza and the menora.
In addition, the verse states, “There is length of days in its right hand; in its left there are wealth and honor” (Prov. 3:17). “Length of days” refers to the World to Come which was given to Israel. “Wealth and honor” belonged to Yavan (ancient Greece) the descendant of Yefet. But when the Greeks turned to evil, Israel merited their portion as well. Hence we have the mezuza which mentions length of days on the right; and we light the menora symbolizing our victory over Greece on the left, expressing our hope to receive their wealth and honor for the purpose of serving G‑d.
Another idea is that since the doorway serves for entry as well as departure, while the menora is on the left of the doorway going in, it illuminates the right side going out. That is to say that this lamp sheds light upon us even when we are “outside”, in exile among the nations. And even now, while the Temple is not built, the light of the Chanuka menora illuminates our path in exile.
In a similar light, the original altar was consecrated on the 25th of Kislev, the same day on which Chanuka was later instituted. The mitzva of making a sanctuary for G‑d in which He may dwell in our midst is thereby timeless and every Jew is obliged to yearn daily for the rebuilding of the Temple. One way we do this is by lighting the Chanuka menora in memory of the miracle that occurred during that re-dedication of the Temple. And we place it facing outward on the right, like a person on vigil waiting at the door in anticipation of a long-expected wayfarer’s return.
May we merit the arrival of Mashiach and the restoration of the Final Temple speedily in our days, Amen!