The Misva of lighting the menorah begins fifteen minutes after sunset for one half hour. Yet, on Friday night, we light 20-40 minutes before sunset to avoid the problem of chilul Shabbat. Even though it is not yet the time for the misva, we still light with a beracha.
The Bach (Bayit Hadash, responsa by R. Yoel Sirkes, 1561-1640) marshals this precedent as a proof to his ruling with regard to the misva of Pidyon Haben. He was dealing with a case in which somebody did a Pidyon Haben by giving the Kohen the money one day early, stipulating that the actual Pidyon should not be activated until the next day, which is the proper time for the misva. The Bach ruled that it is permitted to do so. Moreover, one can even recite the beracha when giving the money even though the actual fulfillment of the mitzva is delayed until tomorrow. He bases this ruling on the Halacha that one recites a beracha on Ner Chanukah on Friday afternoon even though the actual misva does not take place until evening.
Many authorities question this analogy between the case of Pidyon Haben and nerot Hanukah. The Yeshuat Yaakov (Halachic work by R. Yaakov Meshulam Ornstein, Poland 1775-1839) distinguishes between the cases by saying that when we light Chanukah candles on Friday afternoon, it is not considered lighting before the time of the misva. The original, "Lechatehila" institution of the Hachamim was to light early on Friday. Since there will always be at least one Erev Shabbat during the course of the eight day holiday, the Hachamim took this into consideration and instituted that the proper time for lighting on Friday is earlier than the rest of the week. Therefore, one can light before sunset and say a beracha. On the other hand, in the case of Pidyon Haben, the misva is only the next day. How can one say a beracha of "vitzivanu," when the time has not yet arrived?
In addition, the Maharai points out that the Bach himself says that in the case of Chanukah, late afternoon after Plag HaMincha is already actually a proper time for lighting all days of Chanukah. Since one can pray Arbit, according to some opinions it is already considered night. Therefore, one can light before sunset with a beracha; whereas with regard to Pidyon Haben, the day before is not yet the time. Thus, the connection between nerot Hanukah and Pidyon Haben is broken.
We can derive a practical Halacha from this discussion. In general, the Halacha is "Kavta, ein zakuk la," i.e. if the Chanukah candles were set up properly and lit, one does not have to rekindle them in the event that they were extinguished immediately after lighting.
The question is does this Halacha of "Kavta ein zakuk la" apply also to lighting on Friday afternoon.
One could argue that since we light early on Friday, the misva has not even been started and one is required to rekindle the candles. However, according to the previous discussion that Friday afternoon after Plag HaMincha is the Lechatehila time, the Halacha of "Kavta" would apply here as well. Just like on the other days, one does not have to relight a menorah that was lit at the proper time, so too, on Friday. This is the basis for Maranís ruling in Siman 674:2 that even on Erev Shabbat, "Kavta ein zakuk la."
However, Hacham Ovadia writes (Hazon Ovadia, Chanukah p. 110) even though one has fulfilled his obligation if the candles blew out, nonetheless, if a person does go back and relight them "Tavo alav Beracha", it is praiseworthy. Of course, if one does relight, he should not repeat the beracha and he should make sure that he still has time before Shabbat and Minha.
1. If the candles of the menorah were extinguished immediately after lighting, one does not have to rekindle them.
2. This applies even on Friday afternoon, when one lights early. However, it is preferable to go back and light when possible.