Chapter 139:18
Chanukah
18. On Saturday night, Havdallah is recited first (after praying
"Maariv"), and then the Chanukah lights are kindled (1). In the synagogue,
[the Chanukah lights] should be kindled before reciting the passage
"V'yiten Lecho."
FOOTNOTES:
(1) Many authorities rule to the contrary, that is, on Motzei Shabbos, the
Chanukah lights are kindled first and then Havdallah is recited. They
provide two reasons for this ruling:
a) Doing so will delay the act of parting from Shabbos, which Havdallah
signifies (It is important to note that even after the appearance of three
stars after Shabbos, one may not perform an activity which is prohibited on
Shabbos, until after one has recited the prayer "Ata Chonantanu" in the
Maariv Sh'mone Esrei, or until one has said the words "Baruch HaMavdil Bein
Kodesh Le'Chol").
b) The act of publicizing the miracle of Chanukah ("pirsumei nisah") should
come before the recitation of Havdallah.
Those who rule that Havdallah comes first hold that the mitzvah which is
performed more frequently always takes precedence ("Todir Ve'eino Todir,
Todir Kodem").
In Synagogue, the custom is to light the Chanukah candles before
Havadallah. When at home, one should conduct oneself according to one's own
minhag. If one doesn't have a minhag, one should perform Havdallah first
and then kindle the Chanukah lights (Halachos of Chanukah by Rav Shimon
Eider, pg 44, based on Aruch Hashulcan 681:2).